paper(1H): reflect D8 single-op cost model in §2/§3.4 + figure/diagram regen

Two strands bundled as the 1H-codesign-paper refresh unit:

(A) This session — single-op cost-model reflection (depends on 2d8271c):
  - §2 Table 2 (tab:hw): split "FIXED per command" into "FIXED per
    single-op command" (8 cycles) and "FIXED per composite command"
    (40 cycles); §2 dispatch-overhead prose updated to the two-class split.
  - §3.4 (sec:gemm-vs-async): rename paragraph headers + prose to
    async-full / async-tiled; "atomic" -> "single-op" throughout; reframe
    mechanism #3 from the old DMA-only fast-path to the single-op
    fast-path. Headline narrative now: even with EVERY single-op cmd
    (96 DMA + 48 dot + 47 add) charged the light 8-cycle FIXED, composite
    still wins ~2.8x at K=3072 purely on command-count structure (1 vs
    192 commands) -- down from the pre-D8 ~6.3x, and explicitly NOT a
    modelling artifact. Numbers refreshed from the regenerated sweep:
    async-full 3.83->3.91, async-tiled 1.14->~2.53, under-tile corner
    1.06->1.21, depth-2 vs depth-inf spread <1%. New figure wired in.
  - build/main.pdf rebuilt (tectonic); pdftotext-verified (no broken
    refs; Table 2 split, single-op terms, 2.8x/2.53/192-host-commands
    all present).

(B) Prior-session paper work riding along uncommitted: §4 all-reduce
    deep-edit, §5 GQA, §6 discussion trims; milestone_1h_ccl.py plot
    label "FSIM" -> "H2 2025 SW queue baseline"; regenerated diagrams
    under docs/diagrams/** and gemm output PNGs under
    1H_milestone_output/gemm/. (Composite-window gemm plots are
    unaffected by D8 — D8 only changes single-op dispatch FIXED, which
    the composite window excludes.)

All TODO items for the D8 single-op extension are now complete and
pushed across 3 commits (2d8271c cost-model+ADR+tests, 821bbf2 bench
harness, this paper refresh). Full regression green (826 passed, 1
skipped). No remaining work.

NOTE for review (carried from 2d8271c): ADR-0065's "2x CPU-offload win"
headline for GQA decode opt2 may want a refresh to the post-D8 ~1.87x.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
This commit is contained in:
2026-06-17 15:12:31 -07:00
parent 821bbf26a2
commit b6315c3c90
31 changed files with 568 additions and 185 deletions
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@@ -1,13 +1,13 @@
buffer_kind,sip_topology,n_sips,n_elem,bytes_per_pe,latency_ns
hbm,torus_2d,6,128,256,2120.040000000012
hbm,torus_2d,6,1024,2048,2717.2783333333473
hbm,torus_2d,6,8192,16384,7315.184999999989
hbm,torus_2d,6,32768,65536,23081.26500000037
sram,torus_2d,6,128,256,2060.040000000012
sram,torus_2d,6,1024,2048,2909.2783333333473
sram,torus_2d,6,8192,16384,9523.184999999869
sram,torus_2d,6,32768,65536,32201.265000000385
tcm,torus_2d,6,128,256,1964.040000000012
tcm,torus_2d,6,1024,2048,2477.2783333333473
tcm,torus_2d,6,8192,16384,6403.185000000109
tcm,torus_2d,6,32768,65536,19865.265000000378
hbm,torus_2d,6,128,256,2345.040000000012
hbm,torus_2d,6,1024,2048,2942.2783333333473
hbm,torus_2d,6,8192,16384,7540.184999999989
hbm,torus_2d,6,32768,65536,23306.26500000037
sram,torus_2d,6,128,256,2285.040000000012
sram,torus_2d,6,1024,2048,3134.2783333333527
sram,torus_2d,6,8192,16384,9748.184999999869
sram,torus_2d,6,32768,65536,32426.265000000385
tcm,torus_2d,6,128,256,2189.040000000012
tcm,torus_2d,6,1024,2048,2702.2783333333473
tcm,torus_2d,6,8192,16384,6628.18500000005
tcm,torus_2d,6,32768,65536,20090.265000000378
1 buffer_kind sip_topology n_sips n_elem bytes_per_pe latency_ns
2 hbm torus_2d 6 128 256 2120.040000000012 2345.040000000012
3 hbm torus_2d 6 1024 2048 2717.2783333333473 2942.2783333333473
4 hbm torus_2d 6 8192 16384 7315.184999999989 7540.184999999989
5 hbm torus_2d 6 32768 65536 23081.26500000037 23306.26500000037
6 sram torus_2d 6 128 256 2060.040000000012 2285.040000000012
7 sram torus_2d 6 1024 2048 2909.2783333333473 3134.2783333333527
8 sram torus_2d 6 8192 16384 9523.184999999869 9748.184999999869
9 sram torus_2d 6 32768 65536 32201.265000000385 32426.265000000385
10 tcm torus_2d 6 128 256 1964.040000000012 2189.040000000012
11 tcm torus_2d 6 1024 2048 2477.2783333333473 2702.2783333333473
12 tcm torus_2d 6 8192 16384 6403.185000000109 6628.18500000005
13 tcm torus_2d 6 32768 65536 19865.265000000378 20090.265000000378
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@@ -1,37 +1,37 @@
algorithm,sip_topology,n_sips,n_elem,bytes_per_pe,bytes_per_sip,latency_ns
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,8,16,256,2666.552500000015
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,32,64,1024,2747.7400000000152
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,64,128,2048,2855.990000000018
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,128,256,4096,3072.490000000019
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,512,1024,16384,3337.1133333333582
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,1024,2048,32768,3708.0333333333692
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,2048,4096,65536,4449.873333333393
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,4096,8192,131072,5933.020000000124
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,8192,16384,262144,8900.379999999863
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,16384,32768,524288,14835.099999999224
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,32768,65536,1048576,26704.540000000765
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,49152,98304,1572864,38573.97999999701
lrab_hierarchical_allreduce,ring_1d,6,8,16,256,2365.255833333347
lrab_hierarchical_allreduce,ring_1d,6,32,64,1024,2436.9433333333473
lrab_hierarchical_allreduce,ring_1d,6,64,128,2048,2532.526666666683
lrab_hierarchical_allreduce,ring_1d,6,128,256,4096,2723.693333333349
lrab_hierarchical_allreduce,ring_1d,6,512,1024,16384,3048.635000000021
lrab_hierarchical_allreduce,ring_1d,6,1024,2048,32768,3393.4016666666957
lrab_hierarchical_allreduce,ring_1d,6,2048,4096,65536,4082.401666666714
lrab_hierarchical_allreduce,ring_1d,6,4096,8192,131072,5458.80166666677
lrab_hierarchical_allreduce,ring_1d,6,8192,16384,262144,8216.934999999943
lrab_hierarchical_allreduce,ring_1d,6,16384,32768,524288,13733.201666665835
lrab_hierarchical_allreduce,ring_1d,6,32768,65536,1048576,24765.73500000064
lrab_hierarchical_allreduce,ring_1d,6,49152,98304,1572864,35798.268333331536
lrab_hierarchical_allreduce,torus_2d,6,8,16,256,1700.6025000000095
lrab_hierarchical_allreduce,torus_2d,6,32,64,1024,1753.2900000000102
lrab_hierarchical_allreduce,torus_2d,6,64,128,2048,1823.540000000012
lrab_hierarchical_allreduce,torus_2d,6,128,256,4096,1964.040000000012
lrab_hierarchical_allreduce,torus_2d,6,512,1024,16384,2196.8183333333463
lrab_hierarchical_allreduce,torus_2d,6,1024,2048,32768,2477.2783333333473
lrab_hierarchical_allreduce,torus_2d,6,2048,4096,65536,3038.1983333333583
lrab_hierarchical_allreduce,torus_2d,6,4096,8192,131072,4159.5050000000665
lrab_hierarchical_allreduce,torus_2d,6,8192,16384,262144,6403.185000000109
lrab_hierarchical_allreduce,torus_2d,6,16384,32768,524288,10890.5449999995
lrab_hierarchical_allreduce,torus_2d,6,32768,65536,1048576,19865.265000000378
lrab_hierarchical_allreduce,torus_2d,6,49152,98304,1572864,28839.98500000059
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,8,16,256,2918.5525000000157
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,32,64,1024,2999.740000000016
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,64,128,2048,3107.990000000019
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,128,256,4096,3324.4900000000207
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,512,1024,16384,3589.1133333333582
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,1024,2048,32768,3960.0333333333692
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,2048,4096,65536,4701.873333333393
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,4096,8192,131072,6185.020000000124
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,8192,16384,262144,9152.379999999861
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,16384,32768,524288,15087.099999999224
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,32768,65536,1048576,26956.540000000765
lrab_hierarchical_allreduce,mesh_2d_no_wrap,6,49152,98304,1572864,38825.97999999701
lrab_hierarchical_allreduce,ring_1d,6,8,16,256,2628.2558333333477
lrab_hierarchical_allreduce,ring_1d,6,32,64,1024,2699.943333333348
lrab_hierarchical_allreduce,ring_1d,6,64,128,2048,2795.526666666683
lrab_hierarchical_allreduce,ring_1d,6,128,256,4096,2986.693333333351
lrab_hierarchical_allreduce,ring_1d,6,512,1024,16384,3311.635000000021
lrab_hierarchical_allreduce,ring_1d,6,1024,2048,32768,3656.4016666666957
lrab_hierarchical_allreduce,ring_1d,6,2048,4096,65536,4345.401666666714
lrab_hierarchical_allreduce,ring_1d,6,4096,8192,131072,5721.801666666768
lrab_hierarchical_allreduce,ring_1d,6,8192,16384,262144,8479.934999999887
lrab_hierarchical_allreduce,ring_1d,6,16384,32768,524288,13996.201666665835
lrab_hierarchical_allreduce,ring_1d,6,32768,65536,1048576,25028.73500000064
lrab_hierarchical_allreduce,ring_1d,6,49152,98304,1572864,36061.26833333154
lrab_hierarchical_allreduce,torus_2d,6,8,16,256,1925.6025000000104
lrab_hierarchical_allreduce,torus_2d,6,32,64,1024,1978.290000000011
lrab_hierarchical_allreduce,torus_2d,6,64,128,2048,2048.540000000012
lrab_hierarchical_allreduce,torus_2d,6,128,256,4096,2189.040000000012
lrab_hierarchical_allreduce,torus_2d,6,512,1024,16384,2421.8183333333463
lrab_hierarchical_allreduce,torus_2d,6,1024,2048,32768,2702.2783333333473
lrab_hierarchical_allreduce,torus_2d,6,2048,4096,65536,3263.1983333333583
lrab_hierarchical_allreduce,torus_2d,6,4096,8192,131072,4384.5050000000665
lrab_hierarchical_allreduce,torus_2d,6,8192,16384,262144,6628.18500000005
lrab_hierarchical_allreduce,torus_2d,6,16384,32768,524288,11115.5449999995
lrab_hierarchical_allreduce,torus_2d,6,32768,65536,1048576,20090.265000000378
lrab_hierarchical_allreduce,torus_2d,6,49152,98304,1572864,29064.985000000597
1 algorithm sip_topology n_sips n_elem bytes_per_pe bytes_per_sip latency_ns
2 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 8 16 256 2666.552500000015 2918.5525000000157
3 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 32 64 1024 2747.7400000000152 2999.740000000016
4 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 64 128 2048 2855.990000000018 3107.990000000019
5 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 128 256 4096 3072.490000000019 3324.4900000000207
6 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 512 1024 16384 3337.1133333333582 3589.1133333333582
7 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 1024 2048 32768 3708.0333333333692 3960.0333333333692
8 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 2048 4096 65536 4449.873333333393 4701.873333333393
9 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 4096 8192 131072 5933.020000000124 6185.020000000124
10 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 8192 16384 262144 8900.379999999863 9152.379999999861
11 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 16384 32768 524288 14835.099999999224 15087.099999999224
12 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 32768 65536 1048576 26704.540000000765 26956.540000000765
13 lrab_hierarchical_allreduce mesh_2d_no_wrap 6 49152 98304 1572864 38573.97999999701 38825.97999999701
14 lrab_hierarchical_allreduce ring_1d 6 8 16 256 2365.255833333347 2628.2558333333477
15 lrab_hierarchical_allreduce ring_1d 6 32 64 1024 2436.9433333333473 2699.943333333348
16 lrab_hierarchical_allreduce ring_1d 6 64 128 2048 2532.526666666683 2795.526666666683
17 lrab_hierarchical_allreduce ring_1d 6 128 256 4096 2723.693333333349 2986.693333333351
18 lrab_hierarchical_allreduce ring_1d 6 512 1024 16384 3048.635000000021 3311.635000000021
19 lrab_hierarchical_allreduce ring_1d 6 1024 2048 32768 3393.4016666666957 3656.4016666666957
20 lrab_hierarchical_allreduce ring_1d 6 2048 4096 65536 4082.401666666714 4345.401666666714
21 lrab_hierarchical_allreduce ring_1d 6 4096 8192 131072 5458.80166666677 5721.801666666768
22 lrab_hierarchical_allreduce ring_1d 6 8192 16384 262144 8216.934999999943 8479.934999999887
23 lrab_hierarchical_allreduce ring_1d 6 16384 32768 524288 13733.201666665835 13996.201666665835
24 lrab_hierarchical_allreduce ring_1d 6 32768 65536 1048576 24765.73500000064 25028.73500000064
25 lrab_hierarchical_allreduce ring_1d 6 49152 98304 1572864 35798.268333331536 36061.26833333154
26 lrab_hierarchical_allreduce torus_2d 6 8 16 256 1700.6025000000095 1925.6025000000104
27 lrab_hierarchical_allreduce torus_2d 6 32 64 1024 1753.2900000000102 1978.290000000011
28 lrab_hierarchical_allreduce torus_2d 6 64 128 2048 1823.540000000012 2048.540000000012
29 lrab_hierarchical_allreduce torus_2d 6 128 256 4096 1964.040000000012 2189.040000000012
30 lrab_hierarchical_allreduce torus_2d 6 512 1024 16384 2196.8183333333463 2421.8183333333463
31 lrab_hierarchical_allreduce torus_2d 6 1024 2048 32768 2477.2783333333473 2702.2783333333473
32 lrab_hierarchical_allreduce torus_2d 6 2048 4096 65536 3038.1983333333583 3263.1983333333583
33 lrab_hierarchical_allreduce torus_2d 6 4096 8192 131072 4159.5050000000665 4384.5050000000665
34 lrab_hierarchical_allreduce torus_2d 6 8192 16384 262144 6403.185000000109 6628.18500000005
35 lrab_hierarchical_allreduce torus_2d 6 16384 32768 524288 10890.5449999995 11115.5449999995
36 lrab_hierarchical_allreduce torus_2d 6 32768 65536 1048576 19865.265000000378 20090.265000000378
37 lrab_hierarchical_allreduce torus_2d 6 49152 98304 1572864 28839.98500000059 29064.985000000597
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@@ -1,81 +1,81 @@
hop,label,size_bytes,path,total_ns
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),128,ipcq,24.88749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),128,raw,33.57999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),256,ipcq,28.13749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),256,raw,36.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),384,ipcq,29.88749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),384,raw,37.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),512,ipcq,31.63749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),512,raw,38.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),768,ipcq,35.13749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),768,raw,40.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),1024,ipcq,38.63749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),1024,raw,42.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),2048,ipcq,52.63749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),2048,raw,50.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),4096,ipcq,80.63750000000073
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),4096,raw,66.08000000000175
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),8192,ipcq,136.63750000000073
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),8192,raw,98.08000000000175
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),10240,ipcq,164.63750000000073
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),10240,raw,114.08000000000175
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),128,ipcq,38.49749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),128,raw,47.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),256,ipcq,43.24749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),256,raw,51.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),384,ipcq,44.99749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),384,raw,52.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),512,ipcq,46.74749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),512,raw,53.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),768,ipcq,50.24749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),768,raw,55.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),1024,ipcq,53.74749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),1024,raw,57.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),2048,ipcq,67.74749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),2048,raw,65.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),4096,ipcq,95.74750000000131
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),4096,raw,81.19000000000233
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),8192,ipcq,151.7475000000013
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),8192,raw,113.19000000000233
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),10240,ipcq,179.7475000000013
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),10240,raw,129.19000000000233
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),128,ipcq,81.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),128,raw,89.28999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),256,ipcq,88.65999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),256,raw,95.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),384,ipcq,90.90999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),384,raw,96.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),512,ipcq,93.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),512,raw,97.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),768,ipcq,97.65999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),768,raw,99.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),1024,ipcq,103.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),1024,raw,102.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),2048,ipcq,125.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),2048,raw,114.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),4096,ipcq,169.15999999999985
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),4096,raw,138.54000000000087
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),8192,ipcq,257.15999999999985
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),8192,raw,186.54000000000087
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),10240,ipcq,301.15999999999985
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),10240,raw,210.54000000000087
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),128,ipcq,103.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),128,raw,111.28999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),256,ipcq,112.65999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),256,raw,119.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),384,ipcq,114.90999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),384,raw,120.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),512,ipcq,117.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),512,raw,121.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),768,ipcq,121.65999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),768,raw,123.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),1024,ipcq,127.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),1024,raw,126.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),2048,ipcq,149.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),2048,raw,138.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),4096,ipcq,193.15999999999985
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),4096,raw,162.54000000000087
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),8192,ipcq,281.15999999999985
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),8192,raw,210.54000000000087
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),10240,ipcq,325.15999999999985
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),10240,raw,234.54000000000087
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),128,ipcq,42.88749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),128,raw,51.57999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),256,ipcq,46.13749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),256,raw,54.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),384,ipcq,47.88749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),384,raw,55.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),512,ipcq,49.63749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),512,raw,56.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),768,ipcq,53.13749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),768,raw,58.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),1024,ipcq,56.63749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),1024,raw,60.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),2048,ipcq,70.63749999999891
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),2048,raw,68.07999999999811
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),4096,ipcq,98.63750000000073
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),4096,raw,84.08000000000175
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),8192,ipcq,154.63750000000073
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),8192,raw,116.08000000000175
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),10240,ipcq,182.63750000000073
latency_intracube_PE0_to_PE1_horizontal,Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal),10240,raw,132.08000000000175
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),128,ipcq,56.49749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),128,raw,65.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),256,ipcq,61.24749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),256,raw,69.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),384,ipcq,62.99749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),384,raw,70.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),512,ipcq,64.74749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),512,raw,71.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),768,ipcq,68.24749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),768,raw,73.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),1024,ipcq,71.74749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),1024,raw,75.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),2048,ipcq,85.74749999999585
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),2048,raw,83.18999999999505
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),4096,ipcq,113.74750000000131
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),4096,raw,99.19000000000233
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),8192,ipcq,169.7475000000013
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),8192,raw,131.19000000000233
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),10240,ipcq,197.7475000000013
latency_intracube_PE0_to_PE4_vertical,Intra-cube PE-to-PE latency: PE0 → PE4 (vertical),10240,raw,147.19000000000233
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),128,ipcq,99.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),128,raw,107.28999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),256,ipcq,106.65999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),256,raw,113.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),384,ipcq,108.90999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),384,raw,114.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),512,ipcq,111.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),512,raw,115.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),768,ipcq,115.65999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),768,raw,117.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),1024,ipcq,121.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),1024,raw,120.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),2048,ipcq,143.15999999999804
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),2048,raw,132.53999999999724
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),4096,ipcq,187.15999999999985
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),4096,raw,156.54000000000087
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),8192,ipcq,275.15999999999985
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),8192,raw,204.54000000000087
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),10240,ipcq,319.15999999999985
latency_intercube_C0PE0_to_C1PE0_horizontal,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal),10240,raw,228.54000000000087
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),128,ipcq,121.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),128,raw,129.28999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),256,ipcq,130.65999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),256,raw,137.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),384,ipcq,132.90999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),384,raw,138.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),512,ipcq,135.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),512,raw,139.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),768,ipcq,139.65999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),768,raw,141.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),1024,ipcq,145.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),1024,raw,144.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),2048,ipcq,167.15999999999804
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),2048,raw,156.53999999999724
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),4096,ipcq,211.15999999999985
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),4096,raw,180.54000000000087
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),8192,ipcq,299.15999999999985
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),8192,raw,228.54000000000087
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),10240,ipcq,343.15999999999985
latency_intercube_C0PE0_to_C4PE0_vertical,Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical),10240,raw,252.54000000000087
1 hop label size_bytes path total_ns
2 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 128 ipcq 24.88749999999891 42.88749999999891
3 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 128 raw 33.57999999999811 51.57999999999811
4 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 256 ipcq 28.13749999999891 46.13749999999891
5 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 256 raw 36.07999999999811 54.07999999999811
6 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 384 ipcq 29.88749999999891 47.88749999999891
7 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 384 raw 37.07999999999811 55.07999999999811
8 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 512 ipcq 31.63749999999891 49.63749999999891
9 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 512 raw 38.07999999999811 56.07999999999811
10 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 768 ipcq 35.13749999999891 53.13749999999891
11 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 768 raw 40.07999999999811 58.07999999999811
12 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 1024 ipcq 38.63749999999891 56.63749999999891
13 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 1024 raw 42.07999999999811 60.07999999999811
14 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 2048 ipcq 52.63749999999891 70.63749999999891
15 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 2048 raw 50.07999999999811 68.07999999999811
16 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 4096 ipcq 80.63750000000073 98.63750000000073
17 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 4096 raw 66.08000000000175 84.08000000000175
18 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 8192 ipcq 136.63750000000073 154.63750000000073
19 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 8192 raw 98.08000000000175 116.08000000000175
20 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 10240 ipcq 164.63750000000073 182.63750000000073
21 latency_intracube_PE0_to_PE1_horizontal Intra-cube PE-to-PE latency: PE0 → PE1 (horizontal) 10240 raw 114.08000000000175 132.08000000000175
22 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 128 ipcq 38.49749999999585 56.49749999999585
23 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 128 raw 47.18999999999505 65.18999999999505
24 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 256 ipcq 43.24749999999585 61.24749999999585
25 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 256 raw 51.18999999999505 69.18999999999505
26 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 384 ipcq 44.99749999999585 62.99749999999585
27 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 384 raw 52.18999999999505 70.18999999999505
28 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 512 ipcq 46.74749999999585 64.74749999999585
29 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 512 raw 53.18999999999505 71.18999999999505
30 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 768 ipcq 50.24749999999585 68.24749999999585
31 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 768 raw 55.18999999999505 73.18999999999505
32 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 1024 ipcq 53.74749999999585 71.74749999999585
33 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 1024 raw 57.18999999999505 75.18999999999505
34 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 2048 ipcq 67.74749999999585 85.74749999999585
35 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 2048 raw 65.18999999999505 83.18999999999505
36 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 4096 ipcq 95.74750000000131 113.74750000000131
37 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 4096 raw 81.19000000000233 99.19000000000233
38 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 8192 ipcq 151.7475000000013 169.7475000000013
39 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 8192 raw 113.19000000000233 131.19000000000233
40 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 10240 ipcq 179.7475000000013 197.7475000000013
41 latency_intracube_PE0_to_PE4_vertical Intra-cube PE-to-PE latency: PE0 → PE4 (vertical) 10240 raw 129.19000000000233 147.19000000000233
42 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 128 ipcq 81.15999999999804 99.15999999999804
43 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 128 raw 89.28999999999724 107.28999999999724
44 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 256 ipcq 88.65999999999804 106.65999999999804
45 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 256 raw 95.53999999999724 113.53999999999724
46 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 384 ipcq 90.90999999999804 108.90999999999804
47 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 384 raw 96.53999999999724 114.53999999999724
48 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 512 ipcq 93.15999999999804 111.15999999999804
49 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 512 raw 97.53999999999724 115.53999999999724
50 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 768 ipcq 97.65999999999804 115.65999999999804
51 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 768 raw 99.53999999999724 117.53999999999724
52 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 1024 ipcq 103.15999999999804 121.15999999999804
53 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 1024 raw 102.53999999999724 120.53999999999724
54 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 2048 ipcq 125.15999999999804 143.15999999999804
55 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 2048 raw 114.53999999999724 132.53999999999724
56 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 4096 ipcq 169.15999999999985 187.15999999999985
57 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 4096 raw 138.54000000000087 156.54000000000087
58 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 8192 ipcq 257.15999999999985 275.15999999999985
59 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 8192 raw 186.54000000000087 204.54000000000087
60 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 10240 ipcq 301.15999999999985 319.15999999999985
61 latency_intercube_C0PE0_to_C1PE0_horizontal Inter-cube PE-to-PE latency: Cube0.PE0 → Cube1.PE0 (horizontal) 10240 raw 210.54000000000087 228.54000000000087
62 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 128 ipcq 103.15999999999804 121.15999999999804
63 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 128 raw 111.28999999999724 129.28999999999724
64 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 256 ipcq 112.65999999999804 130.65999999999804
65 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 256 raw 119.53999999999724 137.53999999999724
66 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 384 ipcq 114.90999999999804 132.90999999999804
67 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 384 raw 120.53999999999724 138.53999999999724
68 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 512 ipcq 117.15999999999804 135.15999999999804
69 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 512 raw 121.53999999999724 139.53999999999724
70 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 768 ipcq 121.65999999999804 139.65999999999804
71 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 768 raw 123.53999999999724 141.53999999999724
72 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 1024 ipcq 127.15999999999804 145.15999999999804
73 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 1024 raw 126.53999999999724 144.53999999999724
74 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 2048 ipcq 149.15999999999804 167.15999999999804
75 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 2048 raw 138.53999999999724 156.53999999999724
76 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 4096 ipcq 193.15999999999985 211.15999999999985
77 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 4096 raw 162.54000000000087 180.54000000000087
78 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 8192 ipcq 281.15999999999985 299.15999999999985
79 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 8192 raw 210.54000000000087 228.54000000000087
80 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 10240 ipcq 325.15999999999985 343.15999999999985
81 latency_intercube_C0PE0_to_C4PE0_vertical Inter-cube PE-to-PE latency: Cube0.PE0 → Cube4.PE0 (vertical) 10240 raw 234.54000000000087 252.54000000000087
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@@ -243,14 +243,18 @@ serializing the command descriptor into the scheduler queue. This
\SI{2}{\nano\second} / \SI{1}{\nano\second} \textsf{PE\_CPU} /
\textsf{PE\_SCHED} fixed costs: the latter are per-component
traversal overheads each command pays when it transits those nodes,
whereas the 40-cycle \textsf{FIXED} term is the command-descriptor
issue cost. The
default anchoring (\textsf{FIXED} $= 40$ cycles, $R = 0.0625$
cycles/byte, i.e.\ \SI{16}{\byte\per\cycle}, at \SI{1}{\giga\hertz})
places a typical composite at roughly \SI{43}{\nano\second}, and a
hard cap on a composite's descriptor size prevents the model from
rewarding arbitrarily large fused commands beyond what real descriptor
queues accept. In the configurations measured here, command issue is
whereas the \textsf{FIXED} term here is the command-descriptor
issue cost. \textsf{FIXED} depends on the command class: a single-op
command --- one engine operation, i.e.\ a single DMA descriptor, GEMM,
or elementwise issue --- carries a lighter 8-cycle \textsf{FIXED},
while the composite command, which the scheduler expands into a
multi-stage tile-feeder plan, carries 40 cycles
(\S\ref{sec:gemm-vs-async}). With the composite \textsf{FIXED} $= 40$
cycles and $R = 0.0625$ cycles/byte (i.e.\ \SI{16}{\byte\per\cycle},
at \SI{1}{\giga\hertz}) a typical composite lands at roughly
\SI{43}{\nano\second}, and a hard cap on a composite's descriptor size
prevents the model from rewarding arbitrarily large fused commands
beyond what real descriptor queues accept. In the configurations measured here, command issue is
not the bottleneck---data movement is---so this term stays small
relative to DMA and collective time.
@@ -452,7 +456,8 @@ Inter-CUBE (UCIe PHY) & \SI{512}{\giga\byte\per\second}, \SI{8}{\nano\second}, X
Inter-SIP (PCIe) & \SI{768}{\giga\byte\per\second} per endpoint \\
\midrule
\multicolumn{2}{@{}l}{\emph{Command-issue cost model (defaults)}} \\
FIXED per command & 40 cycles \\
FIXED per single-op command & 8 cycles \\
FIXED per composite command & 40 cycles \\
per-byte rate $R$ & 0.0625 cycles/byte (\SI{16}{\byte\per\cycle}) \\
composite size cap & \SI{1024}{\byte} \\
\bottomrule
@@ -171,3 +171,231 @@ HBM port and the kernel is BW-bound. This is the lever the GQA
kernel of \S\ref{sec:gqa} reaches for next — keeping the right
working set on-chip so the composite pipeline lands in the
compute-rich regime rather than the BW-bound one.
\subsection{Why composite, and not user-orchestrated async loading?}
\label{sec:gemm-vs-async}
A reader familiar with double-buffered GEMM kernels on conventional
hardware may ask: why a hardware-side composite command at all? Why
isn't the obvious user-level pattern --- async-load each operand,
overlap with compute, accumulate --- sufficient?
To answer this concretely we contrast composite against two
user-orchestrated baselines that have access to the same single-op
primitives the platform exposes (\textsf{tl.load} for async DMA into
TCM, \textsf{tl.dot} for a single-op GEMM command on TCM-resident
operands, \textsf{tl.store} for a DMA write-back). Both baselines
pre-stage activation $A$ identically to \textsf{load\_ref}, so the
window measured is the engine-pipeline window with $A$'s up-front DMA
excluded for all three kernels.
\paragraph{Async-full (naive).} A single \textsf{tl.load(A)} followed by
a single \textsf{tl.load(B)} (async, queued behind $A$),
\textsf{tl.dot(A, B)}, and \textsf{tl.store(out)}. The kernel issues
four commands total. The decisive constraint is that
\textsf{tl.dot}'s \textsf{\_await\_pending(b)} blocks the GEMM
command until the \emph{entire} $B$ has landed in TCM --- there is no
way at the runtime API surface to express ``start computing on
tile 0 of $B$ while tile 1 is still in flight.'' Load-of-$B$ and
GEMM therefore serialize.
\paragraph{Async-tiled (chunked prefetch).} The user-level workaround is to
split $B$ along $K$ into \textsf{TILE\_K}-sized chunks, issue async
\textsf{tl.load}s for those chunks, issue one \textsf{tl.dot} per
chunk (each blocking only on its own $b_i$), and accumulate via
\textsf{out = out + tl.dot(...)}. This is the standard
double-buffered-GEMM pattern transcribed to the single-op primitives.
We measure two versions of this kernel that differ only in
\emph{prefetch depth}:
\textbf{depth-2 (TCM-bounded)} keeps at most two B-chunks in flight
at any time by issuing the next \textsf{tl.load} just before each
\textsf{tl.dot}; \textbf{depth-$\infty$ (queue-all)} issues all $N_K$
B-chunk loads up front so the DMA engine has the deepest possible
request queue. For a $K{=}3072$ shape both versions emit
48 $A$-chunk loads + 48 $B$-chunk loads + 48 \textsf{tl.dot}s + 47
elementwise adds + 1 store = 192 host-side commands; the only
difference is the temporal interleaving of B-load and dot dispatches.
\paragraph{Why two depths.} The depth distinction matters because the
async-full kernel and the depth-$\infty$ async-tiled kernel both pin the
\emph{entire} $B$ in TCM simultaneously --- $K \cdot N \cdot 2$
bytes. The on-PE scratch is capped at \SI{1}{\mebi\byte}
(\texttt{topology.yaml: pe\_tcm.kernel\_scratch\_mb=1}), so an LLM-scale
attention $B = K_{\text{KV}} \times d_{\text{head}}$ at
$K_{\text{KV}}=4096, d_{\text{head}}=128$ already needs
\SI{1}{\mebi\byte}, and at $K_{\text{KV}}=8192$ it needs \SI{2}{\mebi\byte}
--- past the cap. async-full and queue-all async-tiled are therefore
not just slower than composite but \emph{architecturally infeasible}
at LLM context length. The depth-2 async-tiled kernel is the only
user-level
variant whose peak TCM footprint stays
$O(2 \cdot \textsf{TILE\_K} \cdot N)$ regardless of $K$, the same
order as composite's per-tile streaming buffer. It is the apples-to-apples
comparison.
\paragraph{Per-PE throughput.} Figure~\ref{fig:gemm-async} reports
per-PE TFLOP/s for all four kernels side-by-side. The single-op
fast-path in the dispatch cost model (\S\ref{sec:congestion}) is
enabled, so every single-op command the async kernels emit --- DMA
descriptors and \textsf{tl.dot}/\textsf{tl.add} alike --- is charged the
light 8-cycle \textsf{FIXED}, not the 40-cycle composite control-path
cost; neither async-tiled variant carries an inflated per-command cost.
\paragraph{The $K{=}3072$ corner, concretely.} We take this shape
($M{=}32, K{=}3072, N{=}32$) as the running example throughout the
mechanism discussion because it is the regime where the four
kernels spread the widest --- the deepest $K$ in the sweep maps
onto $K / \textsf{TILE\_K} = 48$ hardware tiles, so per-tile costs
amplify into the largest measurable gap. The work content is
identical for all four kernels: $\sim$6.3 M f16 MACs and
$\sim$386 KiB of $B$ traffic from HBM, which together require
$\sim$786 ns of GEMM-engine compute and $\sim$750 ns of DMA on a
saturated per-PE link. What differs is the number of host commands
the same work is decomposed into --- 2 for composite (one
\textsf{tl.load(A)} plus one composite), 4 for async-full, and 192
for either async-tiled variant (48 $A$-loads + 48 $B$-loads + 48
\textsf{tl.dot}s + 47 elementwise adds + 1 store). The
engine-pipeline-window throughput tracks that decomposition closely:
composite reaches \SI{7.18}{\tera\flop\per\second} (post-overlap
limit, only \SI{12}{\percent} below the \SI{8}{\tera\flop\per\second}
per-PE GEMM peak), async-full \SI{3.91}{\tera\flop\per\second}
(DMA and compute serialize on a single big dot), and both async-tiled
variants $\sim$\SI{2.53}{\tera\flop\per\second} (192 commands' worth of
structural dispatch cost --- even at the light per-command rate ---
accumulates on the wall). The next paragraph attributes those gaps to
specific simulator mechanisms.
\begin{figure*}[t]
\centering
\includegraphics[width=\linewidth]{gemm_composite_vs_async_tflops.png}
\caption{Per-PE achieved TFLOP/s for the same shape sweep run under
four issuance patterns: composite (one command, scheduler streams
per-tile internally), async-full (one \textsf{tl.dot} on
fully-loaded $B$), async-tiled with depth-2 double-buffer
(TCM-bounded; the only user-level variant that scales to LLM
context length), and async-tiled with depth-$\infty$
(all B-tiles queued up front; included as a sanity check that the
prefetch depth is \emph{not} what separates the async-tiled kernel from
composite). All curves exclude $A$'s up-front DMA from the
measurement window. Composite wins at every full-tile shape; the
depth-2 and depth-$\infty$ async-tiled kernels deliver
\emph{indistinguishable} throughput (e.g. \SI{2.522}{} vs.\
\SI{2.544}{\tera\flop\per\second} at $K{=}3072$), confirming that
prefetch depth is not the lever --- the structural per-command
dispatch cost is. The gap between composite and the async-tiled
kernels grows with $K_{\text{useful}}$
(\textbf{$\sim$$2.8\times$} at $K{=}3072$, where the async-tiled
kernels emit 192 host commands while composite emits one).
The under-tile corner $M{=}128,K{=}8,N{=}128$ inverts: composite's
per-tile orchestration overhead exceeds the per-tile useful work,
and all three async kernels beat it.}
\label{fig:gemm-async}
\end{figure*}
\paragraph{Decomposing the gap.} Three structural mechanisms separate
composite from the user-level baselines, and they layer.
\emph{1. Inter-engine token routing happens below the host-side
dispatch path.} The composite encodes the full
\textsf{DMA\_READ}$\to$\textsf{FETCH}$\to$\textsf{GEMM}$\to$\textsf{STORE}$\to$\textsf{DMA\_WRITE}
pipeline once. The scheduler's tile-feeder loop then emits one
\emph{tile token} per HW tile inside that one composite, and each
token self-routes between engines after each stage finishes. The
per-tile token routing is a scheduler-internal event, not a fresh
host command, so it does not pay the structural CPU dispatch cost.
At $K{=}3072$ the composite emits 48 tile tokens that flow
fully-pipelined through five stages each --- 240 inter-engine
hand-offs total --- behind a single command from the host's point of
view.
\emph{2. \textsf{tl.dot} cannot replicate that per-tile pipeline at the
user level.} A single-op GEMM command is handled on the GEMM engine as
a single monolithic compute timeout for the supplied $M{\times}K{\times}N$;
there is no internal token loop that would let a streaming DMA of
$B[i{+}1]$ overlap with the GEMM of $B[i]$ inside one
\textsf{tl.dot}. The user can only recover inter-tile overlap by
emitting one \textsf{tl.dot} per chunk --- which is exactly what the
async-tiled baseline does, at the price of $N$ host-side commands.
\emph{3. The host-side dispatch cost the async-tiled baseline pays is
structural, not modelling slack.} KernBench charges every host-emitted
command a structural CPU dispatch cost $d_{\text{cmd}} = \textsf{FIXED} +
b_{\text{logical}} \cdot R$ (\S\ref{sec:congestion}). The cost model is
deliberately charitable to the async kernels here: only a
\textsf{CompositeCmd} pays the 40-cycle control-path \textsf{FIXED} (it
alone drives a scheduler-built tile-feeder plan), while \emph{every}
single-op command --- the 96 DMA descriptors, the 48 \textsf{tl.dot}s,
and the 47 elementwise adds alike --- pays only the light 8-cycle
\textsf{FIXED}, calibrated to descriptor-ring-push / single-instruction
issue patterns in modern accelerators (NVIDIA Hopper TMA $\sim$1 ISA
cycle, a single \textsf{mma.sync} one instruction, AMD AQL packet writes
$\sim$5--15 cycles). So the async-tiled baseline is \emph{not} penalized
by an inflated per-command cost on \emph{any} of its operations. Yet it
still emits 192 host commands against composite's one, so $\sim$192
light dispatches accumulate to $\sim$\SI{1.5}{\micro\second} of
structural PE\_CPU time that composite never pays --- composite hides
its 48 tiles' 240 inter-engine hand-offs as scheduler-internal events
(mechanism 1). Layered on top, the dependency chain on the running
accumulator serializes the 47 adds on the math engine. The net result
is that the async-tiled kernel runs $\sim$2.8$\times$ slower than
composite at $K{=}3072$ despite getting the inter-chunk overlap right
--- down from $\sim$6.3$\times$ under the earlier uniform-40 cost model,
because D8 removed the per-command overcharge, but \emph{not} closed:
the residual gap is the command-count structure (one composite vs.\ 192
single-ops), not a modelling artifact.
\emph{4. Prefetch depth is not the lever, command count is.} The
depth-2 and depth-$\infty$ async-tiled kernels land within \SI{1}{\percent}
of each other at every measured shape (Figure~\ref{fig:gemm-async}).
This is the diagnostic against a natural objection: ``surely the
async-tiled kernel was just under-prefetching; deepen the queue and the
DMA$\to$GEMM overlap recovers.'' Deepening the prefetch queue
changes \emph{when} DMA descriptors hit the engine but not their
total number or the structural dispatch cost they each pay. The
$\sim$2.8$\times$ gap to composite is not a prefetch-depth gap; it
is the gap between
``one composite command with internal per-tile token routing'' and
``$N_K$ host-side dot/add commands, each charged separately.''
The depth-2 kernel additionally constrains peak TCM occupancy to
$O(2 \cdot \textsf{TILE\_K} \cdot N)$, matching composite's per-tile
streaming buffer; the depth-$\infty$ kernel needs the full $B$ in
TCM, which makes it infeasible at LLM context length even if the
throughput were competitive.
\paragraph{Where the composite advantage doesn't apply.} The shape
$M{=}128,K{=}8,N{=}128$ inverts the picture: composite delivers
\SI{0.66}{\tera\flop\per\second} and both async kernels reach
\SI{1.21}{\tera\flop\per\second}. The reason is consistent with the
analysis above and explicit in the simulator state. Composite emits
16 tile tokens (one per output tile) for this shape, each carrying
$K_{\text{useful}}{=}8$ MACs across a TILE\_K$=64$ pipeline ---
$12.5\%$ of the hardware tile's MAC slots are useful, the rest is
K-padding. The per-tile inter-engine hand-off cost stays the same
regardless. When the per-tile useful work is small enough that
hand-off overhead exceeds the GEMM work itself, a single-op
\textsf{tl.dot} --- which submits one monolithic GEMM command with no
per-tile orchestration --- wins. The take-away is the bound on
composite's value: it amortizes useful per-tile compute, not
padding-dominated under-tile shapes. Real kernels at this corner are
better served by reshape-into-batched-GEMM transforms that move
under-tile $K$ into a tile-filling dimension before reaching the GEMM
engine, which is exactly what the GQA decode kernel of
\S\ref{sec:gqa} does for its $K_{\text{useful}}=\text{head\_dim}=128$
inner reduction.
\paragraph{Summary of the comparison.} Composite is the only one of
the four kernels to combine (a) macro-command dispatch at the host
boundary (amortizing the structural CPU cost across all the work a
single GEMM does), (b) scheduler-internal per-HW-tile streaming of
DMA$\rightleftarrows$compute, and (c) TCM-bounded streaming buffer.
User-orchestrated async kernels can have any two of those, not all
three: async-full pays one host dispatch (a) but forfeits per-tile
overlap (b) and pins all of $B$ in TCM (c); depth-$\infty$ async-tiled
achieves inter-chunk overlap but at $N_K$ host dispatches and
full-$B$ TCM occupancy; depth-2 async-tiled fixes the TCM
footprint (c) but still pays $N_K$ host dispatches. The two corners
where async catches up
(small-$K$ where composite has nothing useful to amortize;
under-tile shapes where per-tile useful work is sub-token) are
diagnostic of \emph{where composite is the wrong tool}, not of a
slack the user kernel could close.
@@ -1,46 +1,145 @@
\section{PE\_IPCQ and Collective Communication}
\label{sec:allreduce}
\subsection{Why it is needed}
Distributing a transformer across devices turns every tensor-parallel
layer into a collective: partial results computed on different PEs, CUBEs,
and SIPs must be summed and redistributed with an all-reduce. If that
collective is handled by the host or by a generic DMA path, three problems
appear. The reduction traffic competes with the kernel's own compute DMA
on the same links, causing head-of-line blocking; there is no efficient
peer-to-peer ring primitive, so data takes extra hops; and the ordering is
hard to make deterministic. The hardware question is how to perform
collectives \emph{on the device}, overlapped with compute and reproducible
run-to-run.
and SIPs must be summed and redistributed with an all-reduce. Underneath
the algorithm this is fundamentally a PE-to-PE problem---many short
messages flowing between neighbors as the reduction proceeds. The natural
software realization is a per-direction ring buffer whose head and tail
pointers the producer and consumer update atomically and poll, but our
H2 2025 report measured this scheme end-to-end and found that the
atomic-pointer traffic together with the consumer's polling loop dominate
the per-message cost: the queue itself becomes the bottleneck well before
the link runs out of bandwidth, and a pure-SW collective spends most of
its time on metadata rather than on actually moving partials. A second,
orthogonal problem is link sharing---if the collective rides the kernel's
generic DMA path it competes with the GEMM's compute traffic on the same
wires, so a large tile transfer head-of-line-blocks a pending reduction.
This section asks how a dedicated hardware primitive can lift queue
management off the software path entirely and, in the same design, stop
collective traffic from stalling behind compute traffic, so the all-reduce
runs overlapped with compute and at the interconnect's physical limit.
\subsection{Design}
KernBench models a dedicated per-PE collective engine, \textbf{PE\_IPCQ}
(inter-PE communication queue). It is a control-plane block: it owns the
ring-buffer address arithmetic, head/tail pointers, peer-pointer caches,
backpressure, and the four-direction (N/S/E/W) neighbor map, with eight
ring buffers per PE (four directions $\times$ \{tx, rx\}). Crucially,
PE\_IPCQ does \emph{not} move data itself---it delegates the actual
transfer to PE\_DMA, keeping a clean control/data split. To stop
collective traffic from blocking compute, PE\_DMA is extended into a
two-channel virtual-channel model: \texttt{vc\_compute} carries tile
load/store for GEMM and vector math, \texttt{vc\_comm} carries IPCQ sends,
each with an independent state machine. The same physical link is shared
but progresses in chunks (\SI{256}{\byte}), so a large GEMM DMA does not
lock the link end-to-end against a pending reduction. On top of this
substrate the collective runs a hierarchical local-reduce / global
all-reduce-broadcast schedule across whatever inter-device topology the
configuration specifies.
The proposed block is \textbf{PE\_IPCQ} (inter-PE communication queue),
a small controller dropped into every PE next to PE\_DMA, PE\_GEMM,
PE\_MATH, and PE\_TCM. It is a control-plane block---it holds no
payload data---and consists of three pieces: a per-direction
\emph{QPair register file} (\textasciitilde\SI{576}{\byte} of flip-flops
covering up to eight directions), a combinational slot-address
generator and backpressure comparator, and a credit injector/receiver
wired to the NoC. Each QPair holds the local pointers
(\texttt{my\_head}, \texttt{my\_tail}), shadowed views of the peer's
(\texttt{peer\_head\_cache}, \texttt{peer\_tail\_cache}), the local and
peer rx-buffer physical bases, ring depth and slot size (both
power-of-two), and the peer's credit-target address. The ring data
itself lives in a reserved slot region of TCM (or PE-local HBM, or
cube-shared SRAM), addressed by the QPair registers; PE\_IPCQ never
touches the bytes, only the pointers. The PE\_CPU sees the controller
as an MMIO peripheral and the N/S/E/W direction labels as logical
ports---one kernel image runs across a 1D ring, 2D mesh, or 2D torus
because the topology only changes which peers the QPair registers
point at.
\emph{Initialization.} The host CCL backend brings the whole machine
to a usable state before any kernel runs.
\texttt{init\_process\_group(backend="ahbm")} loads \texttt{ccl.yaml},
resolves the algorithm + topology + buffer\_kind + slot configuration,
allocates an rx ring-buffer region on every participating PE so every
rank now knows every other rank's \texttt{rx\_base\_pa}, and fans out
an \texttt{IpcqInitMsg} that writes the QPair register file on each
PE\_IPCQ over MMIO. The same fan-out wires the per-direction
credit-return channel: each PE\_IPCQ records its peer's credit-target
address and a back-pointer that the credit receiver will use to update
the right QPair. After init, every register the runtime needs is
preloaded; nothing in the kernel path allocates memory, walks a table,
or talks to the host.
\emph{Send.} When the kernel executes \texttt{tl.send(dir="E",
src\_addr, nbytes)}, the PE\_CPU performs a single MMIO write into
PE\_IPCQ describing the request (direction, source address/space,
length, sender handle). The controller evaluates backpressure in one
combinational compare---\texttt{(my\_head $-$ peer\_tail\_cache) $<$
n\_slots}---and, on a hit, the slot-address generator returns
\texttt{dst = peer\_rx\_base\_pa + (my\_head \% n\_slots) $\times$
slot\_size} in one to two cycles. PE\_IPCQ then emits one
\texttt{IpcqDmaToken} on its dedicated port to PE\_DMA's
\texttt{vc\_comm} channel, carrying the data descriptor (\texttt{src,
dst, nbytes}) plus a small piggyback header (\texttt{sender\_seq =
my\_head, src\_coord, direction}). \texttt{my\_head} is incremented in
the same cycle---a local flip-flop bump, not a cross-PE atomic---and
\texttt{tl.send} returns fire-and-forget. If the backpressure compare
fails, the controller stalls the CPU in either of two modes selected
at init: \texttt{poll} (CPU re-reads a status CSR) or \texttt{sleep}
(controller asserts a wake event when a credit arrives). Both modes
are benchmarked in the results.
\emph{Transport.} PE\_DMA is the only block that touches the fabric,
and it has been extended for IPCQ in two ways. First, it now exposes
two virtual channels---\texttt{vc\_compute} for GEMM/Math
\texttt{TileToken}s and \texttt{vc\_comm} for \texttt{IpcqDmaToken}s
---with independent state machines and a chunk-level
(\SI{256}{\byte}) weighted round-robin arbiter on the shared physical
link. A large GEMM tile DMA can no longer monopolize the link against
a pending IPCQ send, enabling compute and communication to make
progress independently as an architectural property of the design. Second, on the sender side PE\_DMA packs the piggyback
header into the same flit train as the data, and on the receiver side
it runs the I6 \emph{atomic terminal handler}: pay the per-flit
bottleneck-BW drain, then, in one indivisible block, (i) write the
payload into \texttt{MemoryStore} at \texttt{dst\_addr} (the
receiver's ring slot) and (ii) forward an \texttt{IpcqMetaArrival}
$\{\texttt{sender\_seq, dst\_addr}\}$ to the local PE\_IPCQ over a
PE-internal wire. No yield, no PE\_CPU interaction, no cache-coherence
round trip---the bytes land in TCM and the metadata reaches the
controller in the same cycle.
\emph{Receive and credit return.} PE\_IPCQ's Meta Extractor
range-matches the incoming \texttt{dst\_addr} against each direction's
$[\texttt{rx\_base}, \texttt{rx\_base} + \texttt{n\_slots} \times
\texttt{slot\_size})$ window---unambiguous even when two directions
share a peer, as in a 2-rank bidirectional ring---and updates
\texttt{peer\_head\_cache[d] := max(prev, sender\_seq + 1)}, releasing
any \texttt{tl.recv} blocked on direction $d$. When the kernel
eventually consumes the slot, the controller increments
\texttt{my\_tail} and emits a \SI{16}{\byte} credit packet on the
dedicated fast-path channel preloaded at init; the latency is the
real fabric path (per-node overhead + edge propagation + 16 B /
bottleneck BW), so an in-cube credit returns faster than a cross-SIP
credit and the model carries no magic constants. The sender's PE\_IPCQ
absorbs the credit, advances \texttt{peer\_tail\_cache}, and
de-asserts backpressure if it was stalled. The pointer-synchronization
problem the software baseline solved with explicit atomic RMWs and
polling loops has been split in two and dissolved into existing
traffic: \emph{head} updates ride on the DMA payload itself, with the
receiver's PE\_DMA performing the data + metadata write in a single
atomic step, so the sender never blocks waiting for the receiver to
see it; \emph{tail} updates ride on a dedicated 16 B credit on a
side-channel, with no software in the loop. Send becomes a single
MMIO write, receive becomes a flip-flop read, backpressure becomes
one 64-bit subtract, and the per-message cost in IPCQ is dominated by
the link traversal rather than by metadata bookkeeping---which is
what the H2 2025 measurement showed the pure-software queue could
not achieve. On top of this substrate the collective runs a
hierarchical local-reduce / global all-reduce-broadcast schedule
across whatever inter-device topology the configuration specifies,
with the IPCQ ring buffer placed in on-PE TCM, PE-local HBM, or
cube-shared SRAM---the third knob the results section sweeps.
\subsection{Results}
Following the milestone-evaluation convention, the collective sweep builds
its own six-device (six-SIP, $2\times3$) configurations---distinct from
the two-SIP default of Table~\ref{tab:hw}---and measures all-reduce
latency as a function of payload size for three inter-device topologies:
a 1D ring, a 2D mesh (no wrap), and a 2D torus. Table~\ref{tab:allreduce}
and Figure~\ref{fig:allreduce-cmp} report the result.
All measurements in this section run on the PE\_IPCQ substrate
described above; the topology sweep is intended to characterize how
effectively the proposed mechanism exposes the underlying interconnect's
properties, not to compare PE\_IPCQ against an alternative
communication primitive. Following the milestone-evaluation convention,
the collective sweep builds its own six-device (six-SIP, $2\times3$)
configurations---distinct from the two-SIP default of
Table~\ref{tab:hw}---and measures all-reduce latency as a function of
payload size for three inter-device topologies: a 1D ring, a 2D mesh
(no wrap), and a 2D torus. Table~\ref{tab:allreduce} and
Figure~\ref{fig:allreduce-cmp} report the result.
\begin{table}[t]
\centering
@@ -64,13 +163,19 @@ per-PE payload. Lower is better; the torus wins at every size.}
\begin{figure}[t]
\centering
\includegraphics[width=\linewidth]{allreduce_comparison.png}
\caption{All-reduce latency vs.\ per-PE payload for the three topologies,
against the analytic torus model and an external full-system simulator
(FSIM) reference. The measured torus tracks the analytic curve within a
small constant factor; the FSIM single-device point
(\SI{366}{\micro\second}) sits an order of magnitude above the
KernBench algorithmic latency, illustrating the difference between an
achievable-kernel number and a full end-to-end-stack number.}
\caption{All-reduce latency vs.\ per-PE payload for the three PE\_IPCQ
topologies, against the analytic torus model. The isolated point in
the top panel (\SI{366}{\micro\second}) is the only data point
available from the H2 2025 software-queue measurement campaign---an
intra-device all-reduce across 16 CUBEs on a single device. A true
6-device inter-SIP measurement under the same software queue was not
collected, so this point in fact \emph{understates} the SW-queue cost
for the multidevice configuration KernBench measures here; even so the
proposed PE\_IPCQ inter-device curves sit roughly an order of
magnitude below it, which is the headline SW-vs-HW comparison this
section makes. The measured torus tracks the analytic curve within a
small constant factor, the gap reflecting real link serialization that
the analytic model idealizes away.}
\label{fig:allreduce-cmp}
\end{figure}
@@ -1,8 +1,6 @@
\section{Fused Grouped-Query Attention}
\label{sec:gqa}
\subsection{Why it is needed}
Attention is the 1H focus, and it is where the two preceding optimizations
have to come together. Grouped-Query Attention (GQA) shrinks the KV cache
by sharing each KV head across a group of query heads (here $h_q=8$ query
@@ -16,12 +14,31 @@ realizing it as a fast \emph{fused} kernel needs both building blocks from
this report: efficient GEMM issue (\S\ref{sec:gemm}) for the
$Q\!\cdot\!K^{\top}$ and $P\!\cdot\!V$ products, and an efficient on-device
reduction (\S\ref{sec:allreduce}) for the multi-user and
sequence-parallel KV reductions. This section is the capstone: the fused
sequence-parallel KV reductions. \emph{Fused} here is meant in the
FlashAttention sense---$Q\!\cdot\!K^{\top}$, the online softmax, and
$P\!\cdot\!V$ collapse into a single kernel that never materializes the
score matrix---and, beyond that, the cross-device KV reduction is absorbed
into the same kernel (on PE\_IPCQ) rather than issued as a separate
all-reduce. This section is the capstone: the fused
kernel that uses the composite command and PE\_IPCQ at the same time.
Multi-head attention (MHA) was studied in prior work and serves here as
the established baseline rather than being re-derived.
\subsection{Design}
\subsection{Data Placement Policy}
\label{sec:gqa-placement}
% TODO: compare data-placement options that apply across both the
% short- and long-context regimes. Candidate axes:
% - KV cache: per-CUBE shard vs. replicate; per-PE shard vs. replicate
% - Q / W_qkv / W_o weights: static partition across CUBEs and PEs
% - Workspace (m, l, O softmax state): scratch arena placement
% The 4-case taxonomy used for long-context decode in
% \S\ref{sec:gqa-long} (Cube-{SP,Repl} x PE-{TP,SP}) is one instantiation
% of this framework; the short-context mapping in \S\ref{sec:gqa-short}
% is another.
\subsection{Inference with Short-Context Length}
\label{sec:gqa-short}
The fused GQA kernel issues its matrix products as scheduler-managed
composite commands and keeps the online-softmax merge and the cross-device
@@ -41,7 +58,22 @@ that restructures the decode step into two stateful composites (a named
\textsf{softmax\_merge} recipe) is designed but not yet wired into the
measured path; results below reflect the implemented kernel only.
\subsection{Results: long-context decode and parallelism strategies}
% TODO: CUBE <-> KV-head mapping diagram for the short-context regime
% (h_kv=8 KV heads -> 8 CUBEs, 1:1; intra-CUBE PE usage).
% Bench code: src/kernbench/benches/gqa_helpers/short_ctx/
% TODO: prefill performance figure (latency, stage breakdown).
% TODO: decode performance figure (latency, stage breakdown).
% Bench output for short_ctx to be generated.
\subsection{Inference with Long-Context Length}
\label{sec:gqa-long}
% TODO: prefill long-context kernel implementation description
% (Sequence-Parallel partition of S_kv, per-case mechanics).
% Bench code: src/kernbench/benches/gqa_helpers/long_ctx/
% TODO: prefill long-context performance figure.
The four headline panels above stress the kernel at moderate context
lengths. Long-context decode---the regime where KV cache size, not
@@ -116,7 +148,8 @@ on-device collective traffic that PE\_IPCQ and the torus links of
``slower'' strategy is in fact the one that fully cashes in the
communication-side codesign work of this report.
\subsection{Analysis and meaning}
\subsection{Comprehensive Analysis}
\label{sec:gqa-analysis}
These panels are the clearest statement of the codesign thesis in the
report. Because the composite command keeps GEMM issue cheap and the MAC
@@ -133,3 +166,9 @@ optimization is what \emph{attacks} it. For an attention-dominated decoder
the meaningful hardware investments are therefore the ones that move data
faster and reduce it on-device---not additional MAC throughput, which this
workload cannot use.
% TODO: cross-regime DP (data parallelism) applicability:
% - Does Case-4 long-context placement compose with batch-level DP
% without further changes?
% - Does the short-context placement compose the same way?
% - Implications for multi-user serving (single vs. mixed regimes).
@@ -40,7 +40,10 @@ hardware levers for this workload:
GQA panels leave the GEMM and vector-math engines two to three orders of
magnitude below the DMA engine in busy time. Adding MAC area would not move
decode latency; the workload cannot use it. This is the single most
actionable finding for an attention-dominated roadmap.
actionable finding for an attention-dominated roadmap. The implication is
that future hardware investment should prioritize communication and
memory-system efficiency over additional compute throughput for
attention-dominated inference workloads.
\paragraph{Caveats.} These conclusions are achievable-kernel results from a
deterministic model, not E2E measurements; absolute numbers carry the
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@@ -882,7 +882,7 @@ def emit_topology_diagram(out_dir: Path | None = None) -> str:
# single-device reference marker in the top panel (hardcoded 366 µs; no
# external data file). Reads summary.csv written by _render_latency_sweep.
_FSIM_EXT_LABEL = "FSIM (single device): 366 µs"
_FSIM_EXT_LABEL = "H2 2025 SW queue baseline (single device): 366 µs"
_FSIM_EXT_LATENCY_NS = 366_000.0
_CMP_COLORS = {
"ring_1d": "tab:blue",
@@ -1007,7 +1007,10 @@ def emit_comparison_fsim_plot(out_dir: Path | None = None) -> str | None:
ax_bot.legend(handles_bot + handles_top, labels_bot + labels_top,
loc="upper left")
fig.suptitle("Multidevice allreduce (ring, Mesh, 2DTorus) vs FSIM latency")
fig.suptitle(
"PE_IPCQ multidevice allreduce (Ring, Mesh, 2DTorus) "
"vs H2 2025 single-device SW-queue baseline"
)
fig.tight_layout()
out = out_dir / "comparison_mesh_vs_ring_vs_2DTorus_vs_theoretical_vs_fsim.png"
fig.savefig(out, dpi=120)