Demystifying ARM SME to Optimize General Matrix Multiplications(arxiv.org)
arxiv.org
Demystifying ARM SME to Optimize General Matrix Multiplications
https://arxiv.org/abs/2512.21473
20 comments
ARM SME as implemented on the Apple M4 is quite interesting. Super useful for matrix math (as this paper illustrates well), but my attempts at using the SSVE extension for vector math were an utter failure for performance, despite the increased vector width (512 bits vs. 128 bits for NEON). Potentially the switch into/out of streaming mode is too expensive, but my microbenchmarks indicated the SSVE instructions themselves just didn't have great throughput.
SSVE instructions are executed by the SME engine, which trades latency for throughput. SSVE is really intended to support use of SME, rather than as a replacement for Advanced SIMD on the CPU core itself.
The Apple Silicon CPU Optimization Guide has a lot of great information on SME and SSVE, along with more general information on optimizing for Apple's CPUs
A few quotes from Apple's guide that are particularly relevant to SSVE, from "SSVE Vector Execution Unit Optimization":
> Broadly, this unit is designed to support long vector and matrix operations performed on ZA storage _in the SME Processing Grid_.
> Recommendation: Use SSVE in a supporting role to enable high throughput SME grid computation.
> [Magnitude: High | Applicability: High] SSVE offers wide 64B vectors. While the ISA includes instructions that can operate on multi-vectors, the throughput is often only one 64B vector per cycle. Use SSVE to enable SME, which offers higher parallelism.
> Because of non-speculative execution, communication latencies, and in some cases long memory and computation latencies, SME engine instructions trail execution in the core by dozens to thousands of cycles. Any core compute instructions that consume data produced by the SME engine may have to wait an indeterminate (but long) amount of time for the data to arrive.
The Apple Silicon CPU Optimization Guide has a lot of great information on SME and SSVE, along with more general information on optimizing for Apple's CPUs
A few quotes from Apple's guide that are particularly relevant to SSVE, from "SSVE Vector Execution Unit Optimization":
> Broadly, this unit is designed to support long vector and matrix operations performed on ZA storage _in the SME Processing Grid_.
> Recommendation: Use SSVE in a supporting role to enable high throughput SME grid computation.
> [Magnitude: High | Applicability: High] SSVE offers wide 64B vectors. While the ISA includes instructions that can operate on multi-vectors, the throughput is often only one 64B vector per cycle. Use SSVE to enable SME, which offers higher parallelism.
> Because of non-speculative execution, communication latencies, and in some cases long memory and computation latencies, SME engine instructions trail execution in the core by dozens to thousands of cycles. Any core compute instructions that consume data produced by the SME engine may have to wait an indeterminate (but long) amount of time for the data to arrive.
That makes a ton of sense and aligns with my observations. Thanks for the resource :)
If SSVE is slow, I was hoping that SME instructions could be used in a vector-like fashion (e.g. add two matrices with high throughput, or a Hadamard/element-wise product) but it seems most matrix accelerator ISAs don't have that.
If SSVE is slow, I was hoping that SME instructions could be used in a vector-like fashion (e.g. add two matrices with high throughput, or a Hadamard/element-wise product) but it seems most matrix accelerator ISAs don't have that.
There are SME / SME2 instructions that use the ZA tiles as vector registers / vector groups. These can take advantage of the higher throughput of the SME processing grid vs SSVE instructions that operate on Z registers. See the `FMLA (SME2)` case under Peak Performance at https://scalable.uni-jena.de/opt/sme/micro.html#peak-perform....
Are there any such instructions with 16-bit output? I'm looking for fast addition and subtraction of 16-bit integer vectors
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I was struck by the "Magnitude: High | Applicability: High" bit. Who writes like this? More importantly, who reads like this? The V4 doc (which I have yet to read, but I did a text search) has 64 occurences of this sort of phrasing; not actually all that many, given that there's 293 pages, but enough to be interesting. I wonder if this extra stuff is there to make LLMs pay particular attention.
Intel's software optimization guides have similar annotations on many of their guidelines, and have done since long before LLMs were a thing. As a reader it's useful to know how impactful a given recommendation is and how generally applicable it is without having to read the more detailed explanations.
Ahh, interesting, thanks. (I read the reference manuals but typically ignore the rest... I don't need to write this stuff, just read it!) I've seen people recommend creating docs to be LLM-friendly and I was wondering if this was an instance of that.
I don’t get why they didn’t compare against BLIS. I know you can only do so many benchmarks, and people will often complain no matter what, but BLIS is the obvious comparison. Maybe BLIS doesn’t have kernels for their platform, but they’d be well served by just mentioning that fact to get that question out of the reader’s head.
BLIS even has mixed precision interfaces. But might not cover more exotic stuff like low-precision ints? So this paper could have had a chance to “put some points on the board” against a real top-tier competitor.
BLIS even has mixed precision interfaces. But might not cover more exotic stuff like low-precision ints? So this paper could have had a chance to “put some points on the board” against a real top-tier competitor.
BLIS doesn't appear to support SME: https://github.com/search?q=repo%3Aflame%2Fblis+mopa&type=co...
Maybe you want a comparison anyways, but it won't be competitive. On Apple CPUs, SME is ~8x faster than a single regular CPU core with a good BLAS library.
Maybe you want a comparison anyways, but it won't be competitive. On Apple CPUs, SME is ~8x faster than a single regular CPU core with a good BLAS library.
A bit off-topic for this thread... but very relevant for acceleration: Are you the author of http://livespice.org/ ? Where can we reach you?
Yes I am, you can reach me at [email protected]
Is there a version of this that supports sparse LU solves?
I’m trying to make sense of this question.
GEMMs are dense O(N^3) work operations that have roughly the same access pattern and data reuse properties across all matrices. Of course, I’m simplifying things a lot here; tall-skinny and short-fat patterns are much harder to get performance out of but the spirit of the approach is the same as big square matrices.
Sparse LU solves have a different character. There is nowhere near O(N^3) work. You typically expect something closer to O(N^2) but getting performance out of these operations is notoriously difficult because it depends a lot on the sparsity pattern of the linear system. Making matters worse is that you may commonly have a sparse A that factorises to dense L and/or U matrices.
GEMMs are dense O(N^3) work operations that have roughly the same access pattern and data reuse properties across all matrices. Of course, I’m simplifying things a lot here; tall-skinny and short-fat patterns are much harder to get performance out of but the spirit of the approach is the same as big square matrices.
Sparse LU solves have a different character. There is nowhere near O(N^3) work. You typically expect something closer to O(N^2) but getting performance out of these operations is notoriously difficult because it depends a lot on the sparsity pattern of the linear system. Making matters worse is that you may commonly have a sparse A that factorises to dense L and/or U matrices.
I'm working with small matrices (e.g. 10x10 to 100x100), where I believe the effect of caches/pipelines/registers/etc will kick in before the O(N^2)-vs-O(N^3) discussion. Then dispatching to the hardware accelerators (SME2 FMLA or AMX FMA) and doing a _dense_ solve with 512-bit vectors could still be faster than a sparse solve at small matrix sizes or NEON.
Though as mentioned elsewhere in the thread, these accelerators only offer throughput, and latency suffers...
Though as mentioned elsewhere in the thread, these accelerators only offer throughput, and latency suffers...
This will save us from the nvidia monster!
And then we can have our DRAM back!!!
> MpGEMM achieves an average speedup of 1.23x over the vendor-optimized Apple Accelerate library and significantly outperforms other open-source alternatives.
Don't hold your breath.
Don't hold your breath.