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[KMCompiler][Nvidia] add operator linalg_lu_factor - #4945

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[KMCompiler][Nvidia] add operator linalg_lu_factor#4945
YangLong114514 wants to merge 25 commits into
flagos-ai:masterfrom
YangLong114514:KMCompiler-linalg_lu_factor

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@YangLong114514 YangLong114514 commented Jul 24, 2026

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PR Category

Operator

Type of Change

Other

Description

Add operator linalg_lu_factor with triton.
Computes the LU decomposition of a matrix with partial pivoting. Given input A (*, m, n), returns the compact LU matrix and pivot indices (*, min(m,n), int32), satisfying P @ A = L @ U. L is implicitly stored as a unit lower-triangular matrix in the lower part of LU; U is stored in the upper part. Supports pivot=False to disable pivoting (CUDA only).

Issue

Progress

  • Change is properly reviewed (1 reviewer required, 2 recommended).
  • Change is responded to an issue.
  • Change is fully covered by a UT.

Performance

test_linalg_lu_factor.py
Operator: linalg_lu_factor  Performance Test (dtype=torch.float32, mode=kernel,level=comprehensive)
Status       Torch Latency (ms)    Gems Latency (ms)         Gems Speedup          Size Detail
-----------------------------------------------------------------------------------------------
SUCCESS               0.064656            0.021792               2.967          ([torch.Size([16, 16])], {'pivot': True})
SUCCESS               0.070112            0.013632               5.143          ([torch.Size([16, 16])], {'pivot': False})
SUCCESS               0.086528            0.050240               1.722          ([torch.Size([32, 32])], {'pivot': True})
SUCCESS               0.071248            0.029728               2.397          ([torch.Size([32, 32])], {'pivot': False})
SUCCESS               0.127808            0.155072               0.824          ([torch.Size([64, 64])], {'pivot': True})
SUCCESS               0.070944            0.086560               0.820          ([torch.Size([64, 64])], {'pivot': False})
SUCCESS               0.214432            0.583872               0.367          ([torch.Size([128, 128])], {'pivot': True})
SUCCESS               0.097408            0.134176               0.726          ([torch.Size([128, 128])], {'pivot': False})
SUCCESS               0.408256            1.523168               0.268          ([torch.Size([256, 256])], {'pivot': True})
SUCCESS               0.140752            1.028960               0.137          ([torch.Size([256, 256])], {'pivot': False})
SUCCESS               7.762320            2.945776               2.635          ([torch.Size([1024, 512])], {'pivot': True})
SUCCESS               1.893728            1.478832               1.281          ([torch.Size([1024, 512])], {'pivot': False})
SUCCESS               0.107296            0.025232               4.252          ([torch.Size([32, 16])], {'pivot': True})
SUCCESS               0.068832            0.017472               3.940          ([torch.Size([32, 16])], {'pivot': False})
SUCCESS               0.113856            0.025536               4.459          ([torch.Size([16, 32])], {'pivot': True})
SUCCESS               0.075360            0.015904               4.738          ([torch.Size([16, 32])], {'pivot': False})
SUCCESS               0.326016            0.171392               1.902          ([torch.Size([128, 64])], {'pivot': True})
SUCCESS               0.123744            0.078080               1.585          ([torch.Size([128, 64])], {'pivot': False})
SUCCESS               0.367392            0.256448               1.433          ([torch.Size([64, 128])], {'pivot': True})
SUCCESS               0.174848            0.106368               1.644          ([torch.Size([64, 128])], {'pivot': False})
SUCCESS               0.061184            0.050368               1.215          ([torch.Size([4, 32, 32])], {'pivot': True})
SUCCESS               0.052672            0.029792               1.768          ([torch.Size([4, 32, 32])], {'pivot': False})
SUCCESS               0.045312            0.023200               1.953          ([torch.Size([128, 16, 16])], {'pivot': True})
SUCCESS               0.045456            0.014784               3.075          ([torch.Size([128, 16, 16])], {'pivot': False})
SUCCESS              35.109056           37.323967               0.941          ([torch.Size([1024, 512, 512])], {'pivot': True})
SUCCESS              18.171968           26.555040               0.684          ([torch.Size([1024, 512, 512])], {'pivot': False})
SUCCESS             128.263489          144.178818               0.890          ([torch.Size([4096, 512, 512])], {'pivot': True})
SUCCESS              66.834274          103.271805               0.647          ([torch.Size([4096, 512, 512])], {'pivot': False})


Operator: linalg_lu_factor  Performance Test (dtype=torch.float64, mode=kernel,level=comprehensive)
Status       Torch Latency (ms)    Gems Latency (ms)         Gems Speedup          Size Detail
-----------------------------------------------------------------------------------------------
SUCCESS               0.071872            0.026912               2.671          ([torch.Size([16, 16])], {'pivot': True})
SUCCESS               0.101792            0.019392               5.249          ([torch.Size([16, 16])], {'pivot': False})
SUCCESS               0.095360            0.057760               1.651          ([torch.Size([32, 32])], {'pivot': True})
SUCCESS               0.103712            0.037824               2.742          ([torch.Size([32, 32])], {'pivot': False})
SUCCESS               0.145952            0.172736               0.845          ([torch.Size([64, 64])], {'pivot': True})
SUCCESS               0.112928            0.128352               0.880          ([torch.Size([64, 64])], {'pivot': False})
SUCCESS               0.261568            0.729184               0.359          ([torch.Size([128, 128])], {'pivot': True})
SUCCESS               0.291440            0.279744               1.042          ([torch.Size([128, 128])], {'pivot': False})
SUCCESS               0.647136            1.605216               0.403          ([torch.Size([256, 256])], {'pivot': True})
SUCCESS               0.703360            1.191024               0.591          ([torch.Size([256, 256])], {'pivot': False})
SUCCESS               9.551360            4.537216               2.105          ([torch.Size([1024, 512])], {'pivot': True})
SUCCESS               3.759536            1.695520               2.217          ([torch.Size([1024, 512])], {'pivot': False})
SUCCESS               0.129872            0.030464               4.263          ([torch.Size([32, 16])], {'pivot': True})
SUCCESS               0.076320            0.020864               3.658          ([torch.Size([32, 16])], {'pivot': False})
SUCCESS               0.129696            0.036640               3.540          ([torch.Size([16, 32])], {'pivot': True})
SUCCESS               0.084368            0.024736               3.411          ([torch.Size([16, 32])], {'pivot': False})
SUCCESS               0.388000            0.237184               1.636          ([torch.Size([128, 64])], {'pivot': True})
SUCCESS               0.166528            0.160096               1.040          ([torch.Size([128, 64])], {'pivot': False})
SUCCESS               0.423264            0.282880               1.496          ([torch.Size([64, 128])], {'pivot': True})
SUCCESS               0.216224            0.177024               1.221          ([torch.Size([64, 128])], {'pivot': False})
SUCCESS               0.078624            0.058016               1.355          ([torch.Size([4, 32, 32])], {'pivot': True})
SUCCESS               0.062784            0.037920               1.656          ([torch.Size([4, 32, 32])], {'pivot': False})
SUCCESS               0.061088            0.032512               1.879          ([torch.Size([128, 16, 16])], {'pivot': True})
SUCCESS               0.058272            0.022528               2.587          ([torch.Size([128, 16, 16])], {'pivot': False})
SUCCESS             191.890244           38.351360               5.003          ([torch.Size([1024, 512, 512])], {'pivot': True})
SUCCESS             171.316925           30.698463               5.581          ([torch.Size([1024, 512, 512])], {'pivot': False})
SUCCESS             751.502991          148.350876               5.066          ([torch.Size([4096, 512, 512])], {'pivot': True})
SUCCESS             669.608276          119.028770               5.626          ([torch.Size([4096, 512, 512])], {'pivot': False})


Operator: linalg_lu_factor_out  Performance Test (dtype=torch.float32, mode=kernel,level=comprehensive)
Status       Torch Latency (ms)    Gems Latency (ms)         Gems Speedup          Size Detail
-----------------------------------------------------------------------------------------------
SUCCESS               0.061440            0.021760               2.824          ([torch.Size([16, 16])], {'pivot': True, 'out': [torch.Size([16, 16]), torch.Size([16])]})
SUCCESS               0.073440            0.013696               5.362          ([torch.Size([16, 16])], {'pivot': False, 'out': [torch.Size([16, 16]), torch.Size([16])]})
SUCCESS               0.083520            0.050208               1.663          ([torch.Size([32, 32])], {'pivot': True, 'out': [torch.Size([32, 32]), torch.Size([32])]})
SUCCESS               0.073120            0.029536               2.476          ([torch.Size([32, 32])], {'pivot': False, 'out': [torch.Size([32, 32]), torch.Size([32])]})
SUCCESS               0.125184            0.154720               0.809          ([torch.Size([64, 64])], {'pivot': True, 'out': [torch.Size([64, 64]), torch.Size([64])]})
SUCCESS               0.072992            0.086368               0.845          ([torch.Size([64, 64])], {'pivot': False, 'out': [torch.Size([64, 64]), torch.Size([64])]})
SUCCESS               0.215104            0.579808               0.371          ([torch.Size([128, 128])], {'pivot': True, 'out': [torch.Size([128, 128]), torch.Size([128])]})
SUCCESS               0.097888            0.134176               0.730          ([torch.Size([128, 128])], {'pivot': False, 'out': [torch.Size([128, 128]), torch.Size([128])]})
SUCCESS               0.405440            1.527488               0.265          ([torch.Size([256, 256])], {'pivot': True, 'out': [torch.Size([256, 256]), torch.Size([256])]})
SUCCESS               0.139648            1.032560               0.135          ([torch.Size([256, 256])], {'pivot': False, 'out': [torch.Size([256, 256]), torch.Size([256])]})
SUCCESS               7.353504            2.930576               2.509          ([torch.Size([1024, 512])], {'pivot': True, 'out': [torch.Size([1024, 512]), torch.Size([512])]})
SUCCESS               1.842512            1.619568               1.138          ([torch.Size([1024, 512])], {'pivot': False, 'out': [torch.Size([1024, 512]), torch.Size([512])]})
SUCCESS               0.109184            0.025536               4.276          ([torch.Size([32, 16])], {'pivot': True, 'out': [torch.Size([32, 16]), torch.Size([16])]})
SUCCESS               0.074496            0.017792               4.187          ([torch.Size([32, 16])], {'pivot': False, 'out': [torch.Size([32, 16]), torch.Size([16])]})
SUCCESS               0.116928            0.025472               4.590          ([torch.Size([16, 32])], {'pivot': True, 'out': [torch.Size([16, 32]), torch.Size([16])]})
SUCCESS               0.078176            0.015968               4.896          ([torch.Size([16, 32])], {'pivot': False, 'out': [torch.Size([16, 32]), torch.Size([16])]})
SUCCESS               0.321904            0.170880               1.884          ([torch.Size([128, 64])], {'pivot': True, 'out': [torch.Size([128, 64]), torch.Size([64])]})
SUCCESS               0.127680            0.109760               1.163          ([torch.Size([128, 64])], {'pivot': False, 'out': [torch.Size([128, 64]), torch.Size([64])]})
SUCCESS               0.361056            0.256352               1.408          ([torch.Size([64, 128])], {'pivot': True, 'out': [torch.Size([64, 128]), torch.Size([64])]})
SUCCESS               0.175536            0.110240               1.592          ([torch.Size([64, 128])], {'pivot': False, 'out': [torch.Size([64, 128]), torch.Size([64])]})
SUCCESS               0.064592            0.050016               1.291          ([torch.Size([4, 32, 32])], {'pivot': True, 'out': [torch.Size([4, 32, 32]), torch.Size([4, 32])]})
SUCCESS               0.054816            0.029632               1.850          ([torch.Size([4, 32, 32])], {'pivot': False, 'out': [torch.Size([4, 32, 32]), torch.Size([4, 32])]})
SUCCESS               0.048768            0.023136               2.108          ([torch.Size([128, 16, 16])], {'pivot': True, 'out': [torch.Size([128, 16, 16]), torch.Size([128, 16])]})
SUCCESS               0.046656            0.014624               3.190          ([torch.Size([128, 16, 16])], {'pivot': False, 'out': [torch.Size([128, 16, 16]), torch.Size([128, 16])]})
SUCCESS              38.076351           37.257504               1.022          ([torch.Size([1024, 512, 512])], {'pivot': True, 'out': [torch.Size([1024, 512, 512]), torch.Size([1024, 512])]})
SUCCESS              20.318992           26.447680               0.768          ([torch.Size([1024, 512, 512])], {'pivot': False, 'out': [torch.Size([1024, 512, 512]), torch.Size([1024, 512])]})
SUCCESS             135.640930          143.988678               0.942          ([torch.Size([4096, 512, 512])], {'pivot': True, 'out': [torch.Size([4096, 512, 512]), torch.Size([4096, 512])]})
SUCCESS              75.481506          103.056580               0.732          ([torch.Size([4096, 512, 512])], {'pivot': False, 'out': [torch.Size([4096, 512, 512]), torch.Size([4096, 512])]})

Operator: linalg_lu_factor_out  Performance Test (dtype=torch.float64, mode=kernel,level=comprehensive)
Status       Torch Latency (ms)    Gems Latency (ms)         Gems Speedup          Size Detail
-----------------------------------------------------------------------------------------------
SUCCESS               0.068032            0.096512               0.705          ([torch.Size([16, 16])], {'pivot': True, 'out': [torch.Size([16, 16]), torch.Size([16])]})
SUCCESS               0.098112            0.088672               1.106          ([torch.Size([16, 16])], {'pivot': False, 'out': [torch.Size([16, 16]), torch.Size([16])]})
SUCCESS               0.092448            0.109280               0.846          ([torch.Size([32, 32])], {'pivot': True, 'out': [torch.Size([32, 32]), torch.Size([32])]})
SUCCESS               0.105888            0.105376               1.005          ([torch.Size([32, 32])], {'pivot': False, 'out': [torch.Size([32, 32]), torch.Size([32])]})
SUCCESS               0.149472            0.172576               0.866          ([torch.Size([64, 64])], {'pivot': True, 'out': [torch.Size([64, 64]), torch.Size([64])]})
SUCCESS               0.114208            0.128576               0.888          ([torch.Size([64, 64])], {'pivot': False, 'out': [torch.Size([64, 64]), torch.Size([64])]})
SUCCESS               0.264032            0.729216               0.362          ([torch.Size([128, 128])], {'pivot': True, 'out': [torch.Size([128, 128]), torch.Size([128])]})
SUCCESS               0.287456            0.280192               1.026          ([torch.Size([128, 128])], {'pivot': False, 'out': [torch.Size([128, 128]), torch.Size([128])]})
SUCCESS               0.649664            1.600832               0.406          ([torch.Size([256, 256])], {'pivot': True, 'out': [torch.Size([256, 256]), torch.Size([256])]})
SUCCESS               0.705216            1.190208               0.593          ([torch.Size([256, 256])], {'pivot': False, 'out': [torch.Size([256, 256]), torch.Size([256])]})
SUCCESS               9.250032            4.519264               2.047          ([torch.Size([1024, 512])], {'pivot': True, 'out': [torch.Size([1024, 512]), torch.Size([512])]})
SUCCESS               3.758384            1.586720               2.369          ([torch.Size([1024, 512])], {'pivot': False, 'out': [torch.Size([1024, 512]), torch.Size([512])]})
SUCCESS               0.121536            0.098560               1.233          ([torch.Size([32, 16])], {'pivot': True, 'out': [torch.Size([32, 16]), torch.Size([16])]})
SUCCESS               0.079360            0.089728               0.884          ([torch.Size([32, 16])], {'pivot': False, 'out': [torch.Size([32, 16]), torch.Size([16])]})
SUCCESS               0.132512            0.105264               1.259          ([torch.Size([16, 32])], {'pivot': True, 'out': [torch.Size([16, 32]), torch.Size([16])]})
SUCCESS               0.088544            0.092096               0.961          ([torch.Size([16, 32])], {'pivot': False, 'out': [torch.Size([16, 32]), torch.Size([16])]})
SUCCESS               0.386208            0.236736               1.631          ([torch.Size([128, 64])], {'pivot': True, 'out': [torch.Size([128, 64]), torch.Size([64])]})
SUCCESS               0.213312            0.159936               1.334          ([torch.Size([128, 64])], {'pivot': False, 'out': [torch.Size([128, 64]), torch.Size([64])]})
SUCCESS               0.420032            0.283184               1.483          ([torch.Size([64, 128])], {'pivot': True, 'out': [torch.Size([64, 128]), torch.Size([64])]})
SUCCESS               0.217696            0.176960               1.230          ([torch.Size([64, 128])], {'pivot': False, 'out': [torch.Size([64, 128]), torch.Size([64])]})
SUCCESS               0.080128            0.116608               0.687          ([torch.Size([4, 32, 32])], {'pivot': True, 'out': [torch.Size([4, 32, 32]), torch.Size([4, 32])]})
SUCCESS               0.064160            0.111680               0.574          ([torch.Size([4, 32, 32])], {'pivot': False, 'out': [torch.Size([4, 32, 32]), torch.Size([4, 32])]})
SUCCESS               0.064768            0.108400               0.597          ([torch.Size([128, 16, 16])], {'pivot': True, 'out': [torch.Size([128, 16, 16]), torch.Size([128, 16])]})
SUCCESS               0.055872            0.096192               0.581          ([torch.Size([128, 16, 16])], {'pivot': False, 'out': [torch.Size([128, 16, 16]), torch.Size([128, 16])]})
SUCCESS             194.085022           38.248032               5.074          ([torch.Size([1024, 512, 512])], {'pivot': True, 'out': [torch.Size([1024, 512, 512]), torch.Size([1024, 512])]})
SUCCESS             171.838211           30.832191               5.573          ([torch.Size([1024, 512, 512])], {'pivot': False, 'out': [torch.Size([1024, 512, 512]), torch.Size([1024, 512])]})
SUCCESS             760.495239          148.134521               5.134          ([torch.Size([4096, 512, 512])], {'pivot': True, 'out': [torch.Size([4096, 512, 512]), torch.Size([4096, 512])]})
SUCCESS             678.771606          118.811234               5.713          ([torch.Size([4096, 512, 512])], {'pivot': False, 'out': [torch.Size([4096, 512, 512]), torch.Size([4096, 512])]})

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/test | linalg_lu_factor:thead

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/test | linalg_lu_factor:hygon

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/test | linalg_lu_factor:iluvatar

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/test | linalg_lu_factor:metax

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Test Environment

Env Setting Env Setting
Time 2026-08-01 16:36:28 FlagGems 5.3.2.post1.dev64+g58f1403a2
Arch x86_64 OS ubuntu 22.04
Python 3.10.20 Torch 2.9.0
FlagTree 0.5.1+hcu3.1 Triton 3.1.0
Vendor hygon Device cuda

Test Result

Accuracy Result

Summary

Status Duration Total Passed Skipped Failed
Passed 87.42 sec 10 10 0 0

Performance Result

Summary

Status Duration Reason
Passed 319.11 seconds All tests completed.

Benchmark data

Dtype Speedup Base Gems Shape
fp32 6.255 - - -
1.997 0.114 0.057 [[[16,16]],{'pivot':True}]
3.139 0.105 0.033 [[[16,16]],{'pivot':False}]
1.338 0.183 0.137 [[[32,32]],{'pivot':True}]
1.519 0.121 0.080 [[[32,32]],{'pivot':False}]
0.833 0.310 0.372 [[[64,64]],{'pivot':True}]
0.941 0.208 0.221 [[[64,64]],{'pivot':False}]
0.659 0.627 0.952 [[[128,128]],{'pivot':True}]
0.768 0.416 0.541 [[[128,128]],{'pivot':False}]
0.632 1.311 2.074 [[[256,256]],{'pivot':True}]
0.802 0.762 0.951 [[[256,256]],{'pivot':False}]
0.681 3.890 5.711 [[[1024,512]],{'pivot':True}]
0.738 2.157 2.921 [[[1024,512]],{'pivot':False}]
1.942 0.123 0.063 [[[32,16]],{'pivot':True}]
2.920 0.105 0.036 [[[32,16]],{'pivot':False}]
1.776 0.111 0.062 [[[16,32]],{'pivot':True}]
2.676 0.095 0.036 [[[16,32]],{'pivot':False}]
0.894 0.362 0.405 [[[128,64]],{'pivot':True}]
1.131 0.245 0.217 [[[128,64]],{'pivot':False}]
1.658 0.873 0.527 [[[64,128]],{'pivot':True}]
1.861 0.553 0.297 [[[64,128]],{'pivot':False}]
0.950 0.132 0.138 [[[4,32,32]],{'pivot':True}]
1.289 0.104 0.080 [[[4,32,32]],{'pivot':False}]
1.954 0.116 0.059 [[[128,16,16]],{'pivot':True}]
3.298 0.110 0.033 [[[128,16,16]],{'pivot':False}]
36.919 2805.690 75.996 [[[1024,512,512]],{'pivot':True}]
29.793 1488.760 49.970 [[[1024,512,512]],{'pivot':False}]
39.685 11218.884 282.699 [[[4096,512,512]],{'pivot':True}]
32.340 5956.508 184.182 [[[4096,512,512]],{'pivot':False}]

📎 Download the full log here

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Test Environment

Env Setting Env Setting
Time 2026-08-01 16:36:46 FlagGems 5.3.2.post1.dev59+g58f1403a2
Arch x86_64 OS ubuntu 24.04
Python 3.12.13 Torch 2.9.0
FlagTree None Triton 3.5.0
Vendor thead Device cuda

Test Result

Accuracy Result

Summary

Status Duration Total Passed Skipped Failed
Passed 125.22 sec 10 10 0 0

Performance Result

Summary

Status Duration Reason
Passed 335.95 seconds All tests completed.

Benchmark data

Dtype Speedup Base Gems Shape
fp32 7.493 - - -
1.683 0.038 0.023 [[[16,16]],{'pivot':True}]
2.934 0.036 0.012 [[[16,16]],{'pivot':False}]
1.169 0.069 0.059 [[[32,32]],{'pivot':True}]
1.213 0.039 0.032 [[[32,32]],{'pivot':False}]
0.622 0.140 0.225 [[[64,64]],{'pivot':True}]
0.495 0.063 0.128 [[[64,64]],{'pivot':False}]
0.419 0.298 0.712 [[[128,128]],{'pivot':True}]
0.292 0.130 0.444 [[[128,128]],{'pivot':False}]
0.459 0.648 1.413 [[[256,256]],{'pivot':True}]
0.603 0.479 0.795 [[[256,256]],{'pivot':False}]
0.513 2.179 4.245 [[[1024,512]],{'pivot':True}]
2.547 5.916 2.323 [[[1024,512]],{'pivot':False}]
1.482 0.042 0.028 [[[32,16]],{'pivot':True}]
2.387 0.036 0.015 [[[32,16]],{'pivot':False}]
1.619 0.046 0.028 [[[16,32]],{'pivot':True}]
2.368 0.036 0.015 [[[16,32]],{'pivot':False}]
0.630 0.179 0.284 [[[128,64]],{'pivot':True}]
0.793 0.129 0.163 [[[128,64]],{'pivot':False}]
0.433 0.145 0.334 [[[64,128]],{'pivot':True}]
0.356 0.067 0.187 [[[64,128]],{'pivot':False}]
1.259 0.077 0.061 [[[4,32,32]],{'pivot':True}]
1.282 0.043 0.033 [[[4,32,32]],{'pivot':False}]
2.076 0.047 0.023 [[[128,16,16]],{'pivot':True}]
3.303 0.041 0.012 [[[128,16,16]],{'pivot':False}]
31.767 1496.585 47.111 [[[1024,512,512]],{'pivot':True}]
54.226 2013.840 37.138 [[[1024,512,512]],{'pivot':False}]
33.881 5985.705 176.669 [[[4096,512,512]],{'pivot':True}]
58.990 8056.931 136.581 [[[4096,512,512]],{'pivot':False}]

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github-actions Bot commented Aug 1, 2026

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Test Environment

Env Setting Env Setting
Time 2026-08-01 16:41:34 FlagGems 5.3.2.post1.dev59+g58f1403a2
Arch x86_64 OS ubuntu 22.04
Python 3.12.13 Torch 2.8.0+metax3.7.2.0
FlagTree 3.1.0+metax3.7.2.0 Triton 3.1.0
Vendor metax Device cuda

Test Result

Accuracy Result

Summary

Status Duration Total Passed Skipped Failed
Passed 90.02 sec 10 10 0 0

Performance Result

Summary

Status Duration Reason
Timeout 601.22 seconds All tests completed.

Benchmark data

No performance data collected!


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3 participants