AVX2: Document bounds in NTT and invNTT #469

hanno-becker · 2024-12-02T07:26:37Z

Resolves #222

This commit documents the AVX2 assembly for the [inv]NTT in the x86_64 native backend. In particular, it tracks the bounds of data through the various layers.

The invNTT implementation is highly aggressive in terms of minimizing the number of modular reductions, which makes a pen-and-paper analysis rather difficult.

At the last invNTT layer, the bounds reasoning applied is not enough to show absence of overflow. To remedy, an additional reduction is added.

The analysis for the forward NTT is straightforward.

Ultimately, we confirm the absolute bound of 8*MLKEM_Q for the output of forward and inverse NTT; this is the contractual bound that the higher-level C-code is working with.

oqs-bot

Arm Cortex-A76 (Raspberry Pi 5) benchmarks

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`29196` cycles	`29175` cycles	`1.00`
`ML-KEM-512 encaps`	`35819` cycles	`35853` cycles	`1.00`
`ML-KEM-512 decaps`	`46702` cycles	`46654` cycles	`1.00`
`ML-KEM-768 keypair`	`49191` cycles	`49177` cycles	`1.00`
`ML-KEM-768 encaps`	`55788` cycles	`55840` cycles	`1.00`
`ML-KEM-768 decaps`	`71078` cycles	`71008` cycles	`1.00`
`ML-KEM-1024 keypair`	`72097` cycles	`72212` cycles	`1.00`
`ML-KEM-1024 encaps`	`81628` cycles	`81519` cycles	`1.00`
`ML-KEM-1024 decaps`	`101987` cycles	`102036` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Intel Xeon 4th gen (c7i)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`13849` cycles	`13826` cycles	`1.00`
`ML-KEM-512 encaps`	`18185` cycles	`18063` cycles	`1.01`
`ML-KEM-512 decaps`	`24139` cycles	`24004` cycles	`1.01`
`ML-KEM-768 keypair`	`22439` cycles	`22434` cycles	`1.00`
`ML-KEM-768 encaps`	`24500` cycles	`24441` cycles	`1.00`
`ML-KEM-768 decaps`	`32535` cycles	`32445` cycles	`1.00`
`ML-KEM-1024 keypair`	`32133` cycles	`32157` cycles	`1.00`
`ML-KEM-1024 encaps`	`35693` cycles	`35654` cycles	`1.00`
`ML-KEM-1024 decaps`	`47298` cycles	`47250` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Intel Xeon 3rd gen (c6i)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`20319` cycles	`20318` cycles	`1.00`
`ML-KEM-512 encaps`	`27107` cycles	`27066` cycles	`1.00`
`ML-KEM-512 decaps`	`36193` cycles	`36184` cycles	`1.00`
`ML-KEM-768 keypair`	`34850` cycles	`34841` cycles	`1.00`
`ML-KEM-768 encaps`	`38246` cycles	`38138` cycles	`1.00`
`ML-KEM-768 decaps`	`51396` cycles	`51357` cycles	`1.00`
`ML-KEM-1024 keypair`	`48039` cycles	`48087` cycles	`1.00`
`ML-KEM-1024 encaps`	`55259` cycles	`54213` cycles	`1.02`
`ML-KEM-1024 decaps`	`72072` cycles	`72098` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

AMD EPYC 3rd gen (c6a)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`18143` cycles	`18000` cycles	`1.01`
`ML-KEM-512 encaps`	`23115` cycles	`23070` cycles	`1.00`
`ML-KEM-512 decaps`	`30349` cycles	`30404` cycles	`1.00`
`ML-KEM-768 keypair`	`31005` cycles	`31036` cycles	`1.00`
`ML-KEM-768 encaps`	`33974` cycles	`33948` cycles	`1.00`
`ML-KEM-768 decaps`	`44745` cycles	`44836` cycles	`1.00`
`ML-KEM-1024 keypair`	`44672` cycles	`44636` cycles	`1.00`
`ML-KEM-1024 encaps`	`50109` cycles	`49978` cycles	`1.00`
`ML-KEM-1024 decaps`	`64630` cycles	`64674` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'AMD EPYC 3rd gen (c6a)'.
Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.03.

Benchmark suite	Current: `6c644cb`	Previous: `b2c6403`	Ratio
`ML-KEM-768 encaps`	`37303` cycles	`33948` cycles	`1.10`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

AMD EPYC 4th gen (c7a)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`15074` cycles	`15081` cycles	`1.00`
`ML-KEM-512 encaps`	`19795` cycles	`19775` cycles	`1.00`
`ML-KEM-512 decaps`	`26411` cycles	`26426` cycles	`1.00`
`ML-KEM-768 keypair`	`25676` cycles	`25593` cycles	`1.00`
`ML-KEM-768 encaps`	`28216` cycles	`28200` cycles	`1.00`
`ML-KEM-768 decaps`	`38455` cycles	`38171` cycles	`1.01`
`ML-KEM-1024 keypair`	`35732` cycles	`35590` cycles	`1.00`
`ML-KEM-1024 encaps`	`41267` cycles	`40946` cycles	`1.01`
`ML-KEM-1024 decaps`	`54682` cycles	`54551` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Intel Xeon 4th gen (c7i) (no-opt)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`36223` cycles	`36238` cycles	`1.00`
`ML-KEM-512 encaps`	`46498` cycles	`46211` cycles	`1.01`
`ML-KEM-512 decaps`	`61867` cycles	`61564` cycles	`1.00`
`ML-KEM-768 keypair`	`58987` cycles	`59051` cycles	`1.00`
`ML-KEM-768 encaps`	`73020` cycles	`73103` cycles	`1.00`
`ML-KEM-768 decaps`	`91585` cycles	`91700` cycles	`1.00`
`ML-KEM-1024 keypair`	`88574` cycles	`88798` cycles	`1.00`
`ML-KEM-1024 encaps`	`109431` cycles	`109136` cycles	`1.00`
`ML-KEM-1024 decaps`	`133579` cycles	`132893` cycles	`1.01`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Graviton4

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`18268` cycles	`18266` cycles	`1.00`
`ML-KEM-512 encaps`	`22490` cycles	`22477` cycles	`1.00`
`ML-KEM-512 decaps`	`29420` cycles	`29400` cycles	`1.00`
`ML-KEM-768 keypair`	`30756` cycles	`30772` cycles	`1.00`
`ML-KEM-768 encaps`	`34058` cycles	`34057` cycles	`1.00`
`ML-KEM-768 decaps`	`43869` cycles	`43908` cycles	`1.00`
`ML-KEM-1024 keypair`	`44475` cycles	`44483` cycles	`1.00`
`ML-KEM-1024 encaps`	`50220` cycles	`50207` cycles	`1.00`
`ML-KEM-1024 decaps`	`63655` cycles	`63635` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Arm Cortex-A55 (Snapdragon 888) benchmarks

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`58024` cycles	`58010` cycles	`1.00`
`ML-KEM-512 encaps`	`65658` cycles	`65637` cycles	`1.00`
`ML-KEM-512 decaps`	`84333` cycles	`84284` cycles	`1.00`
`ML-KEM-768 keypair`	`98242` cycles	`98320` cycles	`1.00`
`ML-KEM-768 encaps`	`110011` cycles	`110552` cycles	`1.00`
`ML-KEM-768 decaps`	`136662` cycles	`136538` cycles	`1.00`
`ML-KEM-1024 keypair`	`148739` cycles	`149031` cycles	`1.00`
`ML-KEM-1024 encaps`	`166058` cycles	`165978` cycles	`1.00`
`ML-KEM-1024 decaps`	`202392` cycles	`201821` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Intel Xeon 3rd gen (c6i) (no-opt)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`56689` cycles	`56690` cycles	`1.00`
`ML-KEM-512 encaps`	`71736` cycles	`71796` cycles	`1.00`
`ML-KEM-512 decaps`	`96251` cycles	`96315` cycles	`1.00`
`ML-KEM-768 keypair`	`91793` cycles	`91895` cycles	`1.00`
`ML-KEM-768 encaps`	`111401` cycles	`111512` cycles	`1.00`
`ML-KEM-768 decaps`	`144404` cycles	`144626` cycles	`1.00`
`ML-KEM-1024 keypair`	`134664` cycles	`134620` cycles	`1.00`
`ML-KEM-1024 encaps`	`160240` cycles	`160055` cycles	`1.00`
`ML-KEM-1024 decaps`	`201254` cycles	`201479` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

AMD EPYC 4th gen (c7a) (no-opt)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`45768` cycles	`45940` cycles	`1.00`
`ML-KEM-512 encaps`	`58849` cycles	`58757` cycles	`1.00`
`ML-KEM-512 decaps`	`80021` cycles	`79973` cycles	`1.00`
`ML-KEM-768 keypair`	`74675` cycles	`74621` cycles	`1.00`
`ML-KEM-768 encaps`	`91845` cycles	`91441` cycles	`1.00`
`ML-KEM-768 decaps`	`120364` cycles	`120123` cycles	`1.00`
`ML-KEM-1024 keypair`	`109877` cycles	`110170` cycles	`1.00`
`ML-KEM-1024 encaps`	`131139` cycles	`131077` cycles	`1.00`
`ML-KEM-1024 decaps`	`167658` cycles	`167564` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

AMD EPYC 3rd gen (c6a) (no-opt)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`52551` cycles	`52297` cycles	`1.00`
`ML-KEM-512 encaps`	`67427` cycles	`67747` cycles	`1.00`
`ML-KEM-512 decaps`	`92722` cycles	`92585` cycles	`1.00`
`ML-KEM-768 keypair`	`85050` cycles	`84626` cycles	`1.01`
`ML-KEM-768 encaps`	`104160` cycles	`104787` cycles	`0.99`
`ML-KEM-768 decaps`	`137437` cycles	`137690` cycles	`1.00`
`ML-KEM-1024 keypair`	`124904` cycles	`125413` cycles	`1.00`
`ML-KEM-1024 encaps`	`150166` cycles	`149628` cycles	`1.00`
`ML-KEM-1024 decaps`	`192020` cycles	`192160` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Graviton2

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`29201` cycles	`29176` cycles	`1.00`
`ML-KEM-512 encaps`	`35816` cycles	`35859` cycles	`1.00`
`ML-KEM-512 decaps`	`46727` cycles	`46666` cycles	`1.00`
`ML-KEM-768 keypair`	`49202` cycles	`49247` cycles	`1.00`
`ML-KEM-768 encaps`	`55812` cycles	`55930` cycles	`1.00`
`ML-KEM-768 decaps`	`71067` cycles	`71065` cycles	`1.00`
`ML-KEM-1024 keypair`	`72101` cycles	`72173` cycles	`1.00`
`ML-KEM-1024 encaps`	`81618` cycles	`81620` cycles	`1.00`
`ML-KEM-1024 decaps`	`102042` cycles	`102069` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Graviton4 (no-opt)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`41957` cycles	`41913` cycles	`1.00`
`ML-KEM-512 encaps`	`51806` cycles	`51758` cycles	`1.00`
`ML-KEM-512 decaps`	`69322` cycles	`69321` cycles	`1.00`
`ML-KEM-768 keypair`	`69067` cycles	`69069` cycles	`1.00`
`ML-KEM-768 encaps`	`82699` cycles	`82684` cycles	`1.00`
`ML-KEM-768 decaps`	`106408` cycles	`106475` cycles	`1.00`
`ML-KEM-1024 keypair`	`102228` cycles	`102446` cycles	`1.00`
`ML-KEM-1024 encaps`	`120595` cycles	`120643` cycles	`1.00`
`ML-KEM-1024 decaps`	`150588` cycles	`150588` cycles	`1`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Graviton3

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`19029` cycles	`19031` cycles	`1.00`
`ML-KEM-512 encaps`	`23867` cycles	`23841` cycles	`1.00`
`ML-KEM-512 decaps`	`31240` cycles	`31230` cycles	`1.00`
`ML-KEM-768 keypair`	`32332` cycles	`32332` cycles	`1`
`ML-KEM-768 encaps`	`36082` cycles	`36083` cycles	`1.00`
`ML-KEM-768 decaps`	`46487` cycles	`46488` cycles	`1.00`
`ML-KEM-1024 keypair`	`46956` cycles	`46969` cycles	`1.00`
`ML-KEM-1024 encaps`	`53092` cycles	`53088` cycles	`1.00`
`ML-KEM-1024 decaps`	`67380` cycles	`67404` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Graviton2 (no-opt)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`71217` cycles	`71083` cycles	`1.00`
`ML-KEM-512 encaps`	`87802` cycles	`87838` cycles	`1.00`
`ML-KEM-512 decaps`	`118209` cycles	`118147` cycles	`1.00`
`ML-KEM-768 keypair`	`117578` cycles	`117503` cycles	`1.00`
`ML-KEM-768 encaps`	`139343` cycles	`139289` cycles	`1.00`
`ML-KEM-768 decaps`	`180000` cycles	`180001` cycles	`1.00`
`ML-KEM-1024 keypair`	`174961` cycles	`174233` cycles	`1.00`
`ML-KEM-1024 encaps`	`202851` cycles	`201851` cycles	`1.00`
`ML-KEM-1024 decaps`	`254466` cycles	`253746` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Graviton3 (no-opt)

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`45372` cycles	`45361` cycles	`1.00`
`ML-KEM-512 encaps`	`56181` cycles	`56173` cycles	`1.00`
`ML-KEM-512 decaps`	`75115` cycles	`75100` cycles	`1.00`
`ML-KEM-768 keypair`	`74831` cycles	`74868` cycles	`1.00`
`ML-KEM-768 encaps`	`89159` cycles	`89191` cycles	`1.00`
`ML-KEM-768 decaps`	`114542` cycles	`114549` cycles	`1.00`
`ML-KEM-1024 keypair`	`111071` cycles	`111080` cycles	`1.00`
`ML-KEM-1024 encaps`	`129959` cycles	`129991` cycles	`1.00`
`ML-KEM-1024 decaps`	`162524` cycles	`162576` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

oqs-bot

Arm Cortex-A72 (Raspberry Pi 4) benchmarks

Benchmark suite	Current: `a2bf116`	Previous: `b2c6403`	Ratio
`ML-KEM-512 keypair`	`51368` cycles	`51400` cycles	`1.00`
`ML-KEM-512 encaps`	`58332` cycles	`58666` cycles	`0.99`
`ML-KEM-512 decaps`	`75140` cycles	`74987` cycles	`1.00`
`ML-KEM-768 keypair`	`87566` cycles	`87491` cycles	`1.00`
`ML-KEM-768 encaps`	`96622` cycles	`97259` cycles	`0.99`
`ML-KEM-768 decaps`	`120045` cycles	`120726` cycles	`0.99`
`ML-KEM-1024 keypair`	`131183` cycles	`130977` cycles	`1.00`
`ML-KEM-1024 encaps`	`145281` cycles	`145186` cycles	`1.00`
`ML-KEM-1024 decaps`	`177641` cycles	`177592` cycles	`1.00`

This comment was automatically generated by workflow using github-action-benchmark.

This commit documents the AVX2 assembly for the [inv]NTT in the x86_64 native backend. In particular, it tracks the bounds of data through the various layers. The invNTT implementation is highly aggressive in terms of minimizing the number of modular reductions, which makes a pen-and-paper analysis rather difficult. At the last invNTT layer, the bounds reasoning applied is not enough to show absence of overflow. To remedy, an additional reduction is added. The analysis for the forward NTT is straightforward. Ultimately, we confirm the absolute bound of 8*MLKEM_Q for the output of forward and inverse NTT; this is the contractual bound that the higher-level C-code is working with. Signed-off-by: Hanno Becker <[email protected]>

The AVX2 inverse NTT aggressively minimizes the number of modular reductions required. This is correct to our knowledge, but it is difficult to reason about: As the previous commit shows, one has to take into account rather tight bounds for the absolute value of a Montgomery multiplication. This commit adds another modular reduction to the AVX2 inverse NTT. While not strictly necessary, it simplifies the bounds reasoning considerably, and does not come at a meaningful performance cost. Signed-off-by: Hanno Becker <[email protected]>

This commit adds a few comments to the AVX2 assembly for the base multiplication in NTT domain. In particular, it explains that each coefficient in the output of the basemul is bound by 2q in absolute value, and that, thus, the native AVX2 implementation of polyvec_basemul_acc_montgomery_cached_avx2() does not overflow. Signed-off-by: Hanno Becker <[email protected]>

Signed-off-by: Hanno Becker <[email protected]>

mkannwischer

I checked that you have not modified the code except for the added/moved reductions.
I read through the comments and checked that they make sense.

I do not know how to improve the bounds reasoning to avoid these extra reductions - this is something to check with the author.
However, we can go ahead and merge this now and remove the reductions later when we understand it.

mlkem/native/x86_64/shuffle.inc

mkannwischer · 2024-12-02T14:39:02Z

⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'AMD EPYC 3rd gen (c6a)'. Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.03.

Benchmark suite Current: 6c644cb Previous: b2c6403 Ratio
ML-KEM-768 encaps 37303 cycles 33948 cycles 1.10
This comment was automatically generated by workflow using github-action-benchmark.

@hanno-becker - is this benchmark correct or was that some noise? 10% slowdown on single platforms sounds wrong.

Signed-off-by: Hanno Becker <[email protected]>

hanno-becker marked this pull request as ready for review December 2, 2024 07:26

hanno-becker added the benchmark this PR should be benchmarked in CI label Dec 2, 2024

oqs-bot reviewed Dec 2, 2024

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hanno-becker force-pushed the avx2_documentation branch from 6c644cb to b0a95d1 Compare December 2, 2024 08:13

hanno-becker added benchmark this PR should be benchmarked in CI and removed benchmark this PR should be benchmarked in CI labels Dec 2, 2024

hanno-becker requested a review from mkannwischer December 2, 2024 09:19

hanno-becker added 2 commits December 2, 2024 10:51

hanno-becker force-pushed the avx2_documentation branch from 2c4cdd2 to ce51f78 Compare December 2, 2024 10:54

AVX2: Adjust documentation of bounds for native [inv]NTT

c11ea10

Signed-off-by: Hanno Becker <[email protected]>

hanno-becker force-pushed the avx2_documentation branch from ce51f78 to 99f97a5 Compare December 2, 2024 10:59

mkannwischer approved these changes Dec 2, 2024

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mlkem/native/x86_64/shuffle.inc Outdated Show resolved Hide resolved

Adjust AVX2 assembly documentation to C90 block comment style

e90cbe1

Signed-off-by: Hanno Becker <[email protected]>

hanno-becker force-pushed the avx2_documentation branch from 99f97a5 to e90cbe1 Compare December 2, 2024 15:50

hanno-becker merged commit 3ae93fe into main Dec 2, 2024
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hanno-becker deleted the avx2_documentation branch December 2, 2024 16:26

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AVX2: Document bounds in NTT and invNTT #469

AVX2: Document bounds in NTT and invNTT #469

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mkannwischer commented Dec 2, 2024

⚠️ Performance Alert ⚠️

AVX2: Document bounds in NTT and invNTT #469

AVX2: Document bounds in NTT and invNTT #469

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hanno-becker commented Dec 2, 2024 • edited Loading

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Arm Cortex-A76 (Raspberry Pi 5) benchmarks

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Intel Xeon 4th gen (c7i)

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Intel Xeon 3rd gen (c6i)

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AMD EPYC 3rd gen (c6a)

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⚠️ Performance Alert ⚠️

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AMD EPYC 4th gen (c7a)

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Intel Xeon 4th gen (c7i) (no-opt)

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Graviton4

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Arm Cortex-A55 (Snapdragon 888) benchmarks

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Intel Xeon 3rd gen (c6i) (no-opt)

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AMD EPYC 4th gen (c7a) (no-opt)

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AMD EPYC 3rd gen (c6a) (no-opt)

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Graviton2

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Graviton4 (no-opt)

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Graviton3

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Graviton2 (no-opt)

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Graviton3 (no-opt)

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Arm Cortex-A72 (Raspberry Pi 4) benchmarks

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mkannwischer commented Dec 2, 2024

⚠️ Performance Alert ⚠️

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