Add bounds reasoning comments to AVX2 backend #560

jammychiou1 · 2025-10-26T15:04:46Z

Resolves Add bounds reasoning comments to AVX2 backend #528

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Mac Mini (M1, 2020) benchmarks (opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`46245` cycles	`46243` cycles	`1.00`
`ML-DSA-44 sign`	`132702` cycles	`132735` cycles	`1.00`
`ML-DSA-44 verify`	`47876` cycles	`47881` cycles	`1.00`
`ML-DSA-65 keypair`	`81159` cycles	`81166` cycles	`1.00`
`ML-DSA-65 sign`	`219247` cycles	`219290` cycles	`1.00`
`ML-DSA-65 verify`	`80130` cycles	`80129` cycles	`1.00`
`ML-DSA-87 keypair`	`132357` cycles	`132350` cycles	`1.00`
`ML-DSA-87 sign`	`280984` cycles	`280937` cycles	`1.00`
`ML-DSA-87 verify`	`130424` cycles	`130406` cycles	`1.00`

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Mac Mini (M1, 2020) benchmarks (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`115064` cycles	`115058` cycles	`1.00`
`ML-DSA-44 sign`	`431635` cycles	`431665` cycles	`1.00`
`ML-DSA-44 verify`	`122206` cycles	`122172` cycles	`1.00`
`ML-DSA-65 keypair`	`197112` cycles	`197083` cycles	`1.00`
`ML-DSA-65 sign`	`701011` cycles	`701034` cycles	`1.00`
`ML-DSA-65 verify`	`197688` cycles	`197688` cycles	`1`
`ML-DSA-87 keypair`	`325227` cycles	`325219` cycles	`1.00`
`ML-DSA-87 sign`	`884685` cycles	`884692` cycles	`1.00`
`ML-DSA-87 verify`	`328848` cycles	`328850` cycles	`1.00`

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Arm Cortex-A76 (Raspberry Pi 5) benchmarks (opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`115004` cycles	`114982` cycles	`1.00`
`ML-DSA-44 sign`	`377271` cycles	`377314` cycles	`1.00`
`ML-DSA-44 verify`	`120313` cycles	`120175` cycles	`1.00`
`ML-DSA-65 keypair`	`199250` cycles	`199171` cycles	`1.00`
`ML-DSA-65 sign`	`622635` cycles	`622821` cycles	`1.00`
`ML-DSA-65 verify`	`198187` cycles	`198196` cycles	`1.00`
`ML-DSA-87 keypair`	`326349` cycles	`325598` cycles	`1.00`
`ML-DSA-87 sign`	`790980` cycles	`790006` cycles	`1.00`
`ML-DSA-87 verify`	`325253` cycles	`324398` cycles	`1.00`

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Intel Xeon 4th gen (c7i)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`34962` cycles	`35293` cycles	`0.99`
`ML-DSA-44 sign`	`121049` cycles	`120017` cycles	`1.01`
`ML-DSA-44 verify`	`38221` cycles	`38192` cycles	`1.00`
`ML-DSA-65 keypair`	`61665` cycles	`61551` cycles	`1.00`
`ML-DSA-65 sign`	`199507` cycles	`199134` cycles	`1.00`
`ML-DSA-65 verify`	`62246` cycles	`62382` cycles	`1.00`
`ML-DSA-87 keypair`	`95126` cycles	`93721` cycles	`1.01`
`ML-DSA-87 sign`	`235196` cycles	`229923` cycles	`1.02`
`ML-DSA-87 verify`	`93916` cycles	`94024` cycles	`1.00`

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

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`95254` cycles	`94967` cycles	`1.00`
`ML-DSA-44 sign`	`349037` cycles	`348918` cycles	`1.00`
`ML-DSA-44 verify`	`100789` cycles	`100735` cycles	`1.00`
`ML-DSA-65 keypair`	`164263` cycles	`164543` cycles	`1.00`
`ML-DSA-65 sign`	`567230` cycles	`567551` cycles	`1.00`
`ML-DSA-65 verify`	`165474` cycles	`165398` cycles	`1.00`
`ML-DSA-87 keypair`	`266932` cycles	`267562` cycles	`1.00`
`ML-DSA-87 sign`	`722097` cycles	`722682` cycles	`1.00`
`ML-DSA-87 verify`	`272046` cycles	`271670` cycles	`1.00`

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Arm Cortex-A76 (Raspberry Pi 5) benchmarks (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`213333` cycles	`213108` cycles	`1.00`
`ML-DSA-44 sign`	`782029` cycles	`782015` cycles	`1.00`
`ML-DSA-44 verify`	`230092` cycles	`230320` cycles	`1.00`
`ML-DSA-65 keypair`	`384054` cycles	`383982` cycles	`1.00`
`ML-DSA-65 sign`	`1326768` cycles	`1313471` cycles	`1.01`
`ML-DSA-65 verify`	`375377` cycles	`375490` cycles	`1.00`
`ML-DSA-87 keypair`	`605449` cycles	`605206` cycles	`1.00`
`ML-DSA-87 sign`	`1621496` cycles	`1622880` cycles	`1.00`
`ML-DSA-87 verify`	`617407` cycles	`617415` cycles	`1.00`

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Arm Cortex-A72 (Raspberry Pi 4) benchmarks (opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`229297` cycles	`225291` cycles	`1.02`
`ML-DSA-44 sign`	`680601` cycles	`674064` cycles	`1.01`
`ML-DSA-44 verify`	`230038` cycles	`228253` cycles	`1.01`
`ML-DSA-65 keypair`	`392762` cycles	`399283` cycles	`0.98`
`ML-DSA-65 sign`	`1120149` cycles	`1102258` cycles	`1.02`
`ML-DSA-65 verify`	`383658` cycles	`383981` cycles	`1.00`
`ML-DSA-87 keypair`	`663306` cycles	`645046` cycles	`1.03`
`ML-DSA-87 sign`	`1465499` cycles	`1407349` cycles	`1.04`
`ML-DSA-87 verify`	`649376` cycles	`625913` cycles	`1.04`

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Graviton4

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`69406` cycles	`69297` cycles	`1.00`
`ML-DSA-44 sign`	`215066` cycles	`215394` cycles	`1.00`
`ML-DSA-44 verify`	`72872` cycles	`72803` cycles	`1.00`
`ML-DSA-65 keypair`	`123156` cycles	`123048` cycles	`1.00`
`ML-DSA-65 sign`	`353712` cycles	`354049` cycles	`1.00`
`ML-DSA-65 verify`	`120786` cycles	`120878` cycles	`1.00`
`ML-DSA-87 keypair`	`201134` cycles	`200545` cycles	`1.00`
`ML-DSA-87 sign`	`451336` cycles	`451914` cycles	`1.00`
`ML-DSA-87 verify`	`198201` cycles	`198487` cycles	`1.00`

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AMD EPYC 3rd gen (c6a)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`69683` cycles	`69592` cycles	`1.00`
`ML-DSA-44 sign`	`184860` cycles	`185506` cycles	`1.00`
`ML-DSA-44 verify`	`69154` cycles	`69226` cycles	`1.00`
`ML-DSA-65 keypair`	`119441` cycles	`120798` cycles	`0.99`
`ML-DSA-65 sign`	`295459` cycles	`298349` cycles	`0.99`
`ML-DSA-65 verify`	`115470` cycles	`116590` cycles	`0.99`
`ML-DSA-87 keypair`	`201494` cycles	`201311` cycles	`1.00`
`ML-DSA-87 sign`	`385746` cycles	`386042` cycles	`1.00`
`ML-DSA-87 verify`	`193805` cycles	`193658` cycles	`1.00`

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Intel Xeon 3rd gen (c6i)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`57175` cycles	`56967` cycles	`1.00`
`ML-DSA-44 sign`	`180395` cycles	`180312` cycles	`1.00`
`ML-DSA-44 verify`	`61138` cycles	`61223` cycles	`1.00`
`ML-DSA-65 keypair`	`99517` cycles	`99149` cycles	`1.00`
`ML-DSA-65 sign`	`295948` cycles	`296299` cycles	`1.00`
`ML-DSA-65 verify`	`100305` cycles	`100113` cycles	`1.00`
`ML-DSA-87 keypair`	`153336` cycles	`153114` cycles	`1.00`
`ML-DSA-87 sign`	`352913` cycles	`353081` cycles	`1.00`
`ML-DSA-87 verify`	`152140` cycles	`151972` cycles	`1.00`

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Graviton2

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`115166` cycles	`115181` cycles	`1.00`
`ML-DSA-44 sign`	`377510` cycles	`377683` cycles	`1.00`
`ML-DSA-44 verify`	`120392` cycles	`120343` cycles	`1.00`
`ML-DSA-65 keypair`	`199370` cycles	`199283` cycles	`1.00`
`ML-DSA-65 sign`	`623245` cycles	`623012` cycles	`1.00`
`ML-DSA-65 verify`	`198354` cycles	`198353` cycles	`1.00`
`ML-DSA-87 keypair`	`326701` cycles	`326259` cycles	`1.00`
`ML-DSA-87 sign`	`791828` cycles	`790809` cycles	`1.00`
`ML-DSA-87 verify`	`325412` cycles	`324916` cycles	`1.00`

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Graviton3

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`73849` cycles	`73827` cycles	`1.00`
`ML-DSA-44 sign`	`228459` cycles	`228653` cycles	`1.00`
`ML-DSA-44 verify`	`78255` cycles	`78142` cycles	`1.00`
`ML-DSA-65 keypair`	`129816` cycles	`129734` cycles	`1.00`
`ML-DSA-65 sign`	`378404` cycles	`378349` cycles	`1.00`
`ML-DSA-65 verify`	`129311` cycles	`129160` cycles	`1.00`
`ML-DSA-87 keypair`	`208622` cycles	`210617` cycles	`0.99`
`ML-DSA-87 sign`	`479146` cycles	`479575` cycles	`1.00`
`ML-DSA-87 verify`	`208503` cycles	`210205` cycles	`0.99`

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Graviton4 (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`132648` cycles	`132784` cycles	`1.00`
`ML-DSA-44 sign`	`498274` cycles	`498151` cycles	`1.00`
`ML-DSA-44 verify`	`144830` cycles	`144894` cycles	`1.00`
`ML-DSA-65 keypair`	`226547` cycles	`226211` cycles	`1.00`
`ML-DSA-65 sign`	`813539` cycles	`812397` cycles	`1.00`
`ML-DSA-65 verify`	`231077` cycles	`231596` cycles	`1.00`
`ML-DSA-87 keypair`	`374183` cycles	`374501` cycles	`1.00`
`ML-DSA-87 sign`	`1020719` cycles	`1020931` cycles	`1.00`
`ML-DSA-87 verify`	`383566` cycles	`383519` cycles	`1.00`

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

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`135440` cycles	`134965` cycles	`1.00`
`ML-DSA-44 sign`	`539993` cycles	`540181` cycles	`1.00`
`ML-DSA-44 verify`	`148184` cycles	`148325` cycles	`1.00`
`ML-DSA-65 keypair`	`228063` cycles	`227974` cycles	`1.00`
`ML-DSA-65 sign`	`889220` cycles	`893643` cycles	`1.00`
`ML-DSA-65 verify`	`237929` cycles	`237974` cycles	`1.00`
`ML-DSA-87 keypair`	`372971` cycles	`372801` cycles	`1.00`
`ML-DSA-87 sign`	`1106723` cycles	`1105358` cycles	`1.00`
`ML-DSA-87 verify`	`386855` cycles	`387678` cycles	`1.00`

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

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`157988` cycles	`157813` cycles	`1.00`
`ML-DSA-44 sign`	`565277` cycles	`564791` cycles	`1.00`
`ML-DSA-44 verify`	`169766` cycles	`169751` cycles	`1.00`
`ML-DSA-65 keypair`	`270290` cycles	`270498` cycles	`1.00`
`ML-DSA-65 sign`	`925971` cycles	`926242` cycles	`1.00`
`ML-DSA-65 verify`	`276263` cycles	`275901` cycles	`1.00`
`ML-DSA-87 keypair`	`452768` cycles	`453347` cycles	`1.00`
`ML-DSA-87 sign`	`1188324` cycles	`1186402` cycles	`1.00`
`ML-DSA-87 verify`	`461505` cycles	`461198` cycles	`1.00`

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AMD EPYC 4th gen (c7a)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`42686` cycles	`42979` cycles	`0.99`
`ML-DSA-44 sign`	`130695` cycles	`130913` cycles	`1.00`
`ML-DSA-44 verify`	`44216` cycles	`44413` cycles	`1.00`
`ML-DSA-65 keypair`	`72672` cycles	`72353` cycles	`1.00`
`ML-DSA-65 sign`	`210616` cycles	`212806` cycles	`0.99`
`ML-DSA-65 verify`	`73367` cycles	`72915` cycles	`1.01`
`ML-DSA-87 keypair`	`109463` cycles	`109750` cycles	`1.00`
`ML-DSA-87 sign`	`249730` cycles	`248355` cycles	`1.01`
`ML-DSA-87 verify`	`110219` cycles	`111517` cycles	`0.99`

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Arm Cortex-A55 (Snapdragon 888) benchmarks (opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`288553` cycles	`288273` cycles	`1.00`
`ML-DSA-44 sign`	`927585` cycles	`936164` cycles	`0.99`
`ML-DSA-44 verify`	`295250` cycles	`292179` cycles	`1.01`
`ML-DSA-65 keypair`	`487983` cycles	`488081` cycles	`1.00`
`ML-DSA-65 sign`	`1530864` cycles	`1529760` cycles	`1.00`
`ML-DSA-65 verify`	`482983` cycles	`475632` cycles	`1.02`
`ML-DSA-87 keypair`	`831824` cycles	`841156` cycles	`0.99`
`ML-DSA-87 sign`	`2087730` cycles	`2121320` cycles	`0.98`
`ML-DSA-87 verify`	`815092` cycles	`826714` cycles	`0.99`

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Graviton3 (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`138369` cycles	`138318` cycles	`1.00`
`ML-DSA-44 sign`	`492999` cycles	`493648` cycles	`1.00`
`ML-DSA-44 verify`	`148347` cycles	`148347` cycles	`1`
`ML-DSA-65 keypair`	`241732` cycles	`241461` cycles	`1.00`
`ML-DSA-65 sign`	`809768` cycles	`809767` cycles	`1.00`
`ML-DSA-65 verify`	`240679` cycles	`240584` cycles	`1.00`
`ML-DSA-87 keypair`	`395821` cycles	`395729` cycles	`1.00`
`ML-DSA-87 sign`	`1027366` cycles	`1027294` cycles	`1.00`
`ML-DSA-87 verify`	`401516` cycles	`401299` cycles	`1.00`

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Graviton2 (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`213829` cycles	`213522` cycles	`1.00`
`ML-DSA-44 sign`	`782940` cycles	`794930` cycles	`0.98`
`ML-DSA-44 verify`	`230437` cycles	`230022` cycles	`1.00`
`ML-DSA-65 keypair`	`384543` cycles	`384988` cycles	`1.00`
`ML-DSA-65 sign`	`1310640` cycles	`1307299` cycles	`1.00`
`ML-DSA-65 verify`	`375817` cycles	`376399` cycles	`1.00`
`ML-DSA-87 keypair`	`606688` cycles	`605922` cycles	`1.00`
`ML-DSA-87 sign`	`1626018` cycles	`1626375` cycles	`1.00`
`ML-DSA-87 verify`	`618278` cycles	`617623` cycles	`1.00`

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

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`120170` cycles	`120288` cycles	`1.00`
`ML-DSA-44 sign`	`454518` cycles	`453859` cycles	`1.00`
`ML-DSA-44 verify`	`130051` cycles	`130271` cycles	`1.00`
`ML-DSA-65 keypair`	`204928` cycles	`205208` cycles	`1.00`
`ML-DSA-65 sign`	`736614` cycles	`736112` cycles	`1.00`
`ML-DSA-65 verify`	`209739` cycles	`209715` cycles	`1.00`
`ML-DSA-87 keypair`	`337171` cycles	`337055` cycles	`1.00`
`ML-DSA-87 sign`	`928686` cycles	`926156` cycles	`1.00`
`ML-DSA-87 verify`	`345798` cycles	`345516` cycles	`1.00`

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Arm Cortex-A72 (Raspberry Pi 4) benchmarks (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`317365` cycles	`318223` cycles	`1.00`
`ML-DSA-44 sign`	`1224779` cycles	`1227916` cycles	`1.00`
`ML-DSA-44 verify`	`344907` cycles	`339753` cycles	`1.02`
`ML-DSA-65 keypair`	`552815` cycles	`559842` cycles	`0.99`
`ML-DSA-65 sign`	`1909394` cycles	`1942017` cycles	`0.98`
`ML-DSA-65 verify`	`519791` cycles	`529374` cycles	`0.98`
`ML-DSA-87 keypair`	`872331` cycles	`863765` cycles	`1.01`
`ML-DSA-87 sign`	`2478204` cycles	`2444597` cycles	`1.01`
`ML-DSA-87 verify`	`883699` cycles	`863122` cycles	`1.02`

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Arm Cortex-A55 (Snapdragon 888) benchmarks (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`466124` cycles	`464693` cycles	`1.00`
`ML-DSA-44 sign`	`2213126` cycles	`2221355` cycles	`1.00`
`ML-DSA-44 verify`	`550344` cycles	`545927` cycles	`1.01`
`ML-DSA-65 keypair`	`777048` cycles	`776812` cycles	`1.00`
`ML-DSA-65 sign`	`3645043` cycles	`3636149` cycles	`1.00`
`ML-DSA-65 verify`	`849253` cycles	`849524` cycles	`1.00`
`ML-DSA-87 keypair`	`1254730` cycles	`1270549` cycles	`0.99`
`ML-DSA-87 sign`	`4489453` cycles	`4519665` cycles	`0.99`
`ML-DSA-87 verify`	`1370350` cycles	`1380875` cycles	`0.99`

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SpacemiT K1 8 (Banana Pi F3) benchmarks (no-opt)

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-44 keypair`	`822519` cycles	`821707` cycles	`1.00`
`ML-DSA-44 sign`	`3332513` cycles	`3334149` cycles	`1.00`
`ML-DSA-44 verify`	`919075` cycles	`918864` cycles	`1.00`
`ML-DSA-65 keypair`	`1397964` cycles	`1396572` cycles	`1.00`
`ML-DSA-65 sign`	`5447376` cycles	`5443674` cycles	`1.00`
`ML-DSA-65 verify`	`1465026` cycles	`1464453` cycles	`1.00`
`ML-DSA-87 keypair`	`2301172` cycles	`2300947` cycles	`1.00`
`ML-DSA-87 sign`	`6820350` cycles	`6813578` cycles	`1.00`
`ML-DSA-87 verify`	`2402933` cycles	`2397029` cycles	`1.00`

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⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'Arm Cortex-A72 (Raspberry Pi 4) benchmarks (opt)'.
Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.03.

Benchmark suite	Current: `6ca67e1`	Previous: `ee7e1bf`	Ratio
`ML-DSA-87 sign`	`1465499` cycles	`1407349` cycles	`1.04`
`ML-DSA-87 verify`	`649376` cycles	`625913` cycles	`1.04`

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Signed-off-by: jammychiou1 <[email protected]>

The new approach is adapted from our Neon implementation. See <#411 (comment)> for more information on the idea. Bounds reasoning comments are also added. Signed-off-by: jammychiou1 <[email protected]>

Edit some comments while we're at it. Signed-off-by: jammychiou1 <[email protected]>

mkannwischer

Thanks @jammychiou1. I checked the bounds tracking for NTT, iNTT, basemul and everything makes sense to me. Please include some reasoning for the 3q/4 bounds.
It would also be great if you can extend https://github.com/pq-code-package/mlkem-native/blob/main/test/test_bounds.py to demonstrate the 3q/4 bound.

Let's move the decompose changes to a separate follow-up PR, please.

mkannwischer · 2025-11-05T07:47:32Z

dev/x86_64/src/intt.S

+/*
+ * Compute l + h, montmul(h - l, zh) then store the results back to l, h
+ * respectively.
+ *
+ * The general abs bound of Montgomery multiplication is 3q/4.


As discussed offline: Please include reasoing for the 3q/4 bound --- you actually mean Montgomery multiplication by a constant, not general Montgomery multiplication.

mkannwischer · 2025-11-05T07:47:58Z

dev/x86_64/src/ntt.S

+ * Although the general abs bound of Montgomery multiplication is 3q/4, we use
+ * the more convenient bound q here.


Rephrase and reference intt.S for the 3q/4.

jammychiou1 force-pushed the avx2-bound-comments branch from 1fc1bf6 to 1b76629 Compare October 26, 2025 15:09

jammychiou1 changed the title ~~Add bounds reasoning comments to AVX2 ntt/intt~~ Add bounds reasoning comments to AVX2 backend Oct 27, 2025

jammychiou1 force-pushed the avx2-bound-comments branch 2 times, most recently from ca27600 to da40590 Compare November 2, 2025 10:51

jammychiou1 added the benchmark label Nov 2, 2025