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Comment by shihab | Hacker News Reader

Great article!

For context: this WebGPU version achieves ~17% of peak theoretical performance of M2. With CUDA (i.e. CuBLAS), you can reach ~75% of peak performance for same matrix config (without tensor core).

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> you can reach ~75% of peak performance for same matrix config

Not on the same computer, CUDA doesn’t run on the integrated GPU of the Apple M2 Pro.

That's exactly what I was wondering. That cannot be.

Probably more relevant here is that a single CPU core on that computer exceeds 1 tflop/s on gemm with plenty of margin using a single lib call, and leaves the rest of the CPU cores and all of the GPU free to do other work.

OP implemented that stuff with WebGPU. In runtime, that weird language compiles into a compute shader which computes that stuff on GPU.

I believe the point being made was that this could be done in the CPU faster than was achieved here.

Yeah, but not on a single core.

In my desktop computer, I have Ryzen 7 8700G CPU, which has 8 Zen 4 cores, 4.2 GHz base frequency, 65W TDP. Theoretically, when doing FP32 FMA, each CPU core can do 32 FLOP/cycle. At the base frequency, this translates into 134 GFlops per core. You gonna need all 8 cores to achieve 1 theoretical TFlops.

BTW, integrated GPU inside the same 8700G processor can theoretically do 8.2 TFlops FP32.

I am told the numbers above require the core to have a matrix multiply unit (such as SME)

> Theoretically, when doing FP32 FMA, each CPU core can do 32 FLOP/cycle. At the base frequency, this translates into 134 GFlops per core.

Isn't it that zen4 doesn't have "native" support for AVX-512 but "mimics" it through 2x 256-bit FMA units?

Because of this, a single AVX-512 instruction will occupy both FMA units and therefore I think that the theoretical limit for a single zen4 core should be half of the 134 GFLOPS number?

One FMA counts as two floating-point operations: one multiplication and one addition.

According to uops.info, Zen 4 cores can do two 8-wide FMA instructions per cycle, or one 16-wide FMA per cycle. See VFMADD132PS (YMM, YMM, YMM) and VFMADD132PS (ZMM, ZMM, ZMM) respectively, the throughput column is labelled TP. That’s where 32 FLOP/cycle number comes from.

> doesn't have "native" support for AVX-512 but "mimics" it through 2x 256-bit FMA units

That’s correct, AVX512 doesn’t deliver more FLOPs on that CPU. The throughput of 32-byte FMA and 64-byte FMA is the same, 32 FLOP/cycle for FP32 numbers.

> One FMA counts as two floating-point operations: one multiplication and one addition.

Right. This is where the discrepancy comes from. I counted FMA as a single FLOP.

BTW, it’s the same for GPUs. In DXBC shader byte code, mad instruction does FMA. When reporting theoretical FLOPs, GPU vendors count that as 2 float operations.

For example, I have GeForce 4070 Ti Super in my desktop. The chip has 8448 execution units; nVidia calls them CUDA cores but I don’t like the name, the correct number is 66 cores where each core can do 4 wavefronts of 32 threads each. Anyway, these EUs can do one FP32 FMA each cycle, and the boost clock frequency is 2.61 GHz. Multiplying these two numbers results in 22.04928E+12 cycles*EU/second, and nVidia reports 44E+12 FLOPs peak FP32 performance of the GPU.

Nope, no Apple CPU core has such performance.

That single lib call must have used the AMX accelerator, which is separate from the cores and shared by a group of cores.

So that AMX accelerator performance may be greater than of all CPU cores together. AFAIK, some Apple CPUs have one AMX accelerator for the big cores and another AMX accelerator for the smaller cores, but in any case there is no chance to hope that if you have obtained 1 TFLOP/s when running the program on 1 core you will get much more when running it on multiple cores, because all cores of the same type will use the same shared accelerator.

One interesting thing about these newfangled matrix/AI/ML accelerators that’s very rarely mentioned on the internets, they only deliver that many TFLOP because they operate in very low precision.

nVidia tensor cores support int8, couple versions of FP16 (BF16 and the standard IEEE one) and FP19 which they call TensorFloat-32. I think Intel AMX only supports int8 and BF16.

None of them supports FP32 let alone FP64 input numbers, which makes them completely useless for traditional GEMM stuff.

https://github.com/corsix/amx indicates that Apple's AMX supports up to 64-bit FP, but I don't see any performance metrics. They also have the ANE, which is the low-precision ML-focused accelerator.

I wasn’t aware there’re two completely different things from different companies both called AMX. I assumed that AMX: https://en.wikipedia.org/wiki/Advanced_Matrix_Extensions

The Apple’s version is indeed interesting. I wonder why haven’t Apple exposed it to programmers, or implemented a BLAS library on top of that thing?

> I wonder why haven’t Apple exposed it to programmers, or implemented a BLAS library on top of that thing?

Using the Accelerate framework (which includes Apple's BLAS) is the only supported way for programmers to access the AMX. Reverse engineering the instruction set to access it directly is discouraged, because it's not a documented stable interface.

It’s because Apple’s AMX was an early, in-house built version of what was eventually released by Arm as SME. Apple adopted SME in the M4 and dropped AMX, but as long as you were using their Accelerate framework instead of directly writing AMX code (which they told people not to do), you wouldn’t notice.

Now that they’re using “standard” SME, it shouldn’t be a problem to write SME assembly opcodes directly, although I suspect Apple themselves is still probably sparse on the documentation. I’m not aware if there’s any way to use intrinsics or something slightly higher level than inline-ASM, but lower level than the Accelerate framework.

Apple's matrix unit supports FP16, 32, and 64 sources and accumulators.

Right. So, like I said, using one CPU core, you can exceed 1 TFLOP/s, leaving all the other CPU cores and the GPU free for other work.

Top of the line AMD zen5 core can sustain ~80GFLOPS@FP64 and ~160GFLOPS@FP32 using AVX-512, 2x FMA units and ~5Ghz of clock frequency.

This is way way lower than what you claim M2 Pro is capable of and since I'm comparing it against the state-of-the-art datacenter CPU I'm curious how did you get to this number?

M2 Pro core runs at much lower frequency, what it seems to be around ~3.4GHz. And I couldn't find any information about SVE vector widths supported nor number of FMAs.

Your initial claim was ambiguous.

It sounded like you claimed that using only one core you already reach 1 TFLOP/s, implying that you could reach more than that by using more cores, which is false.

Now you have clarified that you actually claim that it is good that when using a single core you can reach the maximum throughput of the shared matrix operation accelerator.

This is correct, but there is no essential difference between this and a Zen 5 CPU that reaches this throughput by using only half of the cores, while having the other half of the cores free to do any other tasks.

What’s the power draw of however many zen 5 cores you have to tie up to hit, say, 1.5tflop/s on sgemm?

(Also, that’s a M2 number, since that’s what OP was talking about. Someone will presumably post M4 benchmarks for BLAS sometime soon, if they haven’t already.)

Yes, that's why I was focusing on percentage of peak hardware performance, not actual flops.

how are you running CUDA on the integrated Apple silicon GPU these days?

You are not.

75% can't be the best we can do. What would reach 100% or nearly 100%? Handcoded assembly?

With GPUs it's not uncommon to run out of memory bandwidth before you max out the theoretical FLOPS. They may have a ton of bandwidth but it's never enough.

That can lead you to some pretty counter-intuitive optimizations because it's often faster to do more compute work if it means you touch less memory in the process.

Shouldn't the roofline inform capacity assessments?

Sure, but rooflines don't account for stuff like memory granularity. You not only have to do a lot of bytes per flop to achieve the necessary arithmetic intensity, you also have to access those bytes in a coalesced way. I.e., you want to access consecutive bytes, which are ideally already in registers.

For sufficiently large GEMM you should never run out of bandwidth before you max out FLOPS if your blocking is organized correctly, because the arithmetic scales like O(n^3) while the memory access scales like O(n^2).

In theory, yes. In practice you will probably be forced to tile your GEMM and incur the penalty of redundant memory accesses.

Sure, but still on each tile, you do O(k^3) compute with O(k^2) memory, and you generally arrange things so that at least one tile is in L1 and at least one other is in L2/LLC (using CPU idioms), so again, you have plenty of bandwidth (typical choices of k are in the ballpark of ~32, and a 32:1 compute to memory ratio is just fine on most hardware, especially if some of those accesses are coming from fast memory)

I don't think so? It is too late for me to actually do the math on this but if you take the degenerate case where the tile size is literally 1 element then you will do as many loads as arithmetic operations. Thus I would consider any sort of fixed tiling (which you would be resigned to due to your caches being of limited size) requiring O(n^3) loads?

> That can lead you to some pretty counter-intuitive optimizations because it's often faster to do more compute work if it means you touch less memory in the process.

It is not specific to the GPUs: this kind of optimizations are pretty common on CPU too where latency kills you and 200 cycles spent wasted on doing compute can actually be faster than a single cache miss trying to fetch data. This is pretty common for many SIMD algorithms actually.

Memory is currently lagging behind compute on almost every type of modern hardware, and it will very likely become worst, not better.

The parameters of the matrix multiply, such as the size of the matrices, impose some limits to how close you can get to the peak theoretical performance in a particular GPU. Not all possible matrix multiplies are equally valuable to optimize a priori, so the hardware is designed to perform best on problems that are financially significant, such as modern LLMs.

As for handcoded assembly, do you believe that it would be financially sound to hand code and maintain thousands of kernels that way, even if you believed that they would be faster?

> As for handcoded assembly, do you believe that it would be financially sound to hand code and maintain thousands of kernels that way, even if you believed that they would be faster?

Why not? We do so for cryptographic primitives and video codecs. And why are you talking about “thousands of kernels”? AI programs only need a small amount of different kernels so it doesn't sound intractable.

> AI programs only need a small amount of different kernels

That is not the case. What appears like a simple matmul operation actually requires these libraries to select which specific kernel out of the many internally available to execute.

If you are curious to learn more, NVidia open sourced a library called Cutlass some years ago. And remember that is only what they are willing to open source.

Is that really different from AV codecs in terms of scale though?

I am not at liberty to discuss more than that.

Yes, you can peek under the hood of cuBLAS and notice that it has dozens of kernels for different problem sizes. It’s not generally the case that when you do h264 at a different crf you have a completely different tiling strategy that you have to implement.

thanks! and yes definitely not at CUDA levels :)

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