ICX Slowdown: Estrin Polynomial Evaluation Mystery

Hey everyone! Today, let's dive into a peculiar issue I've encountered while porting my radix-2 Estrin polynomial evaluation code to the Intel ICX 2024 compiler. We're seeing some unexpected slowdowns for specific polynomial lengths, particularly those just shy of 16*N. It's a bit of a head-scratcher, and I'm hoping we can brainstorm some potential causes and solutions together.

The Curious Case of the 16N-1 Lengths

So, the core of the issue revolves around Estrin's scheme, a clever way to evaluate polynomials in parallel. My implementation is based on a radix-2 approach, which should, in theory, offer decent performance. However, when I compiled and ran the code using the Intel ICX compiler (the 2024 version, to be precise), I noticed a significant performance dip for polynomial lengths that fall just below multiples of 16 (i.e., 16N-1). For lengths that are exact multiples of 16, the performance is pretty much what I'd expect. But these 16N-1 cases? They're noticeably slower, and that's got me puzzled.

Now, let's break down Estrin's scheme a little bit for those who might not be intimately familiar with it. Polynomial evaluation, at its heart, is a series of multiplications and additions. The naive approach involves calculating each term individually (x^n, x^(n-1), and so on) and then multiplying by the corresponding coefficient. This can be quite inefficient, especially for high-degree polynomials. Estrin's scheme, on the other hand, leverages parallelism by breaking the polynomial into smaller sub-polynomials that can be evaluated concurrently. This is particularly well-suited for modern processors with multiple cores or SIMD (Single Instruction, Multiple Data) capabilities. The radix-2 version, which I'm using, specifically divides the polynomial into halves recursively, further enhancing the potential for parallel execution. The idea is beautiful, it's elegant, and it should be fast. That's why this ICX slowdown is so intriguing. We expect that the performance will be stable, especially when we are using radix-2. However, the fact is that when we use ICX, the 16N-1 lengths of polynomials significantly slow down the whole process. This makes us wonder what is the root cause of this problem. It might be that the ICX compiler has some kind of optimization that behaves unexpectedly. Or, it may also be that there are some underlying hardware issues of Intel ICX.

Diving into the Code and Compiler

The code itself, I believe, is sound. I've tested it extensively with other compilers and on different architectures, and it performs as expected. This leads me to suspect that the issue lies either in the interaction between the code and the Intel ICX compiler or potentially in some underlying hardware behavior specific to the ICX architecture. I'm primarily working in C and Visual C++, so the code is fairly low-level. I've been careful to avoid any obvious performance bottlenecks, and I've experimented with various compiler optimization flags to see if they make a difference (spoiler alert: they haven't, at least not in a way that solves the 16N-1 slowdown). The next step is for us to dive into the details of compiler and find the potential reason. We can start by studying the assembly code generated by the ICX compiler. We should also read the document of ICX to know its optimization mechanism. If possible, we can simplify the polynomial to narrow down the cause. For example, we can remove some terms to see whether it still slow down. If it turns out that certain terms have a significant influence on the performance, it may help us know the potential cause.

Potential Culprits and Troubleshooting

So, where do we even begin troubleshooting this? Here are a few potential areas I've been considering:

• Cache behavior: Could the 16N-1 lengths be triggering some kind of cache conflict or cache line misalignment? Perhaps the data access patterns in these specific cases are less cache-friendly, leading to increased memory access latency. This is always the first thing to suspect when we see performance anomalies. Memory access is often the bottleneck of many programs. Cache misses will cause significant performance degradation. Therefore, we should carefully analyze the memory access patterns when the length of polynomials is 16N-1.
• SIMD alignment: Given that Estrin's scheme can benefit from SIMD instructions, is it possible that the 16N-1 lengths are causing alignment issues that hinder SIMD performance? Misaligned data can force the processor to perform multiple memory accesses instead of a single, vectorized operation. To ensure SIMD alignment, we usually need to pad the data size to a power of 2 or multiple of SIMD register length. If the length is 16N-1, it can not be divided by SIMD register length, which probably causes performance problem. Therefore, it makes sense that 16N-1 lengths of polynomials cause a slowdown.
• Compiler optimizations: Is the ICX compiler applying some specific optimization for multiples of 16 that it's not applying to 16N-1? Perhaps there's a loop unrolling or vectorization strategy that's less effective in these cases. Sometimes compiler optimizations might introduce unexpected behavior. For example, some aggressive optimizations may lead to larger code size, which reduces instruction cache hit ratio. Therefore, it's necessary to understand the optimization flags and their potential influence on the performance. In fact, there are cases that aggressive optimization makes the program slower rather than faster.
• ICX microarchitecture: Could there be some quirk in the ICX microarchitecture itself that's contributing to this? Perhaps some specific instruction sequences or memory access patterns are less efficient on ICX than on other architectures. We can consult Intel's optimization manual to see whether there is something that we should pay attention to. Sometimes, the performance bottleneck is caused by the underlying hardware.

To investigate these possibilities, I've been experimenting with:

• Profiling tools: I've used profiling tools to get a better understanding of where the code is spending its time. This has helped me confirm that the slowdown is indeed occurring within the Estrin evaluation function, but it hasn't yet pinpointed the root cause. We can use the profiling results to know which part of the code becomes the performance bottleneck. If we can identify the hot spots, we can focus our efforts on optimizing these parts.
• Assembly code analysis: I've examined the assembly code generated by ICX for both the 16N and 16N-1 cases. This is a deep dive, but it might reveal subtle differences in the generated instructions that explain the performance difference. By analyzing assembly code, we can understand the compiler's optimization strategy. We can also see whether the compiler generates the code we expect. For example, we can check whether SIMD instructions are used properly. If not, we can add some hints to help the compiler generate better code.
• Microbenchmarks: I'm considering writing some microbenchmarks to isolate specific operations (e.g., memory access patterns, SIMD operations) and see how they perform on ICX for different data sizes and alignments. This may help us pinpoint the underlying cause of the problem. Microbenchmarks are helpful for us to measure the performance of small pieces of code. This can isolate the problem and identify the specific operations that become the bottleneck.

Seeking Your Wisdom and Insights

This is where I'm hoping the community can lend a hand. Has anyone else encountered similar performance anomalies with Intel ICX or other compilers when working with polynomial evaluation or other numerical algorithms? Do you have any insights into potential causes or troubleshooting strategies that I haven't considered? Any advice or suggestions would be greatly appreciated!

Specifically, I'm curious about:

• Experiences with ICX: Have you noticed any other unexpected performance behaviors with the Intel ICX compiler? Are there any known quirks or gotchas that I should be aware of?
• Polynomial evaluation optimization: Are there any specific optimization techniques that are particularly effective (or ineffective) for Estrin's scheme or other polynomial evaluation methods on modern architectures?
• Cache and SIMD considerations: Do you have any tips for ensuring optimal cache utilization and SIMD alignment when working with numerical algorithms?

Let's put our heads together and crack this mystery! I'll be sure to share any progress I make, and I'm eager to hear your thoughts and suggestions. Thanks in advance for your help, guys!

Updates and Further Investigations

I wanted to provide a quick update on my investigation into the ICX slowdown. I've been digging deeper into the assembly code and experimenting with different compiler flags, and I've made a few interesting observations.

First, it seems that the ICX compiler is indeed applying some aggressive loop unrolling and vectorization for the multiples-of-16 cases. This is likely contributing to the better performance I'm seeing for those lengths. However, for the 16N-1 cases, the compiler seems to be falling back to a more scalar-based approach, which could explain the slowdown. This may be caused by the fact that the length 16N-1 is not a multiple of SIMD vector length. Therefore, the remaining data cannot be handled using SIMD instructions. Scalar code is much slower than SIMD code. So this might be the reason.

Second, I've noticed some differences in the way memory is accessed in the two cases. The 16N cases seem to have more predictable and aligned memory access patterns, which is beneficial for cache utilization. The 16N-1 cases, on the other hand, seem to have more scattered and potentially misaligned accesses. As we discussed, memory access is very important for performance. If there are too many cache misses, the performance will degrade significantly.

I'm now focusing my efforts on trying to guide the compiler towards generating more vectorized code for the 16N-1 cases. I'm experimenting with directives and pragmas that can influence the compiler's optimization decisions. I'm also looking into ways to improve the memory access patterns, perhaps by padding the data or using different data structures. We can try to add some directives to the code to help the compiler generate more efficient code. For example, we can use #pragma omp simd to tell the compiler to generate SIMD code. We can also use alignas to align the data to a specific memory address. These hints may help the compiler generate better code.

I'll keep you updated on my progress. If you have any further suggestions or insights, please don't hesitate to share them!

Conclusion and Next Steps

The mystery of the ICX slowdown for Estrin polynomial evaluation with lengths 16N-1 continues! We've explored several potential causes, including cache behavior, SIMD alignment, compiler optimizations, and even ICX microarchitecture quirks. While we haven't yet pinpointed the exact culprit, we've made some progress in understanding the problem.

My next steps will be to:

• Continue experimenting with compiler directives and pragmas to try to force vectorization for the 16N-1 cases.
• Refine my microbenchmarks to isolate specific memory access patterns and SIMD operations.
• Explore alternative polynomial evaluation schemes to see if they exhibit the same behavior on ICX.

I'm still open to any suggestions or insights you might have. Let's keep the conversation going and hopefully solve this puzzle together! Thanks again for all your help and support, guys!