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GPU Implementations of Online Track Finding Algorithms at PANDA

AndiH
March 21, 2014

GPU Implementations of Online Track Finding Algorithms at PANDA

A 12 minutes talk I gave at the spring meeting of the German Physical Society in Frankfurt 2014. The status of my PhD thesis. More or less.

AndiH

March 21, 2014
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  1. Mitglied der Helmholtz-Gemeinschaft
    GPU Implementations of
    Online Track Finding
    Algorithms at PANDA
    1
    HK 57.2, DPG-Frühjahrstagung 2014, Frankfurt
    21 March 2014, Andreas Herten (Institut für Kernphysik, Forschungszentrum Jülich) for the PANDA Collaboration

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  2. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    PANDA — The Experiment
    2
    13 m

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  3. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    PANDA — The Experiment
    2
    13 m
    Magnet
    STT
    MVD

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  4. Mitglied der Helmholtz-Gemeinschaft
    PANDA — Event Reconstruction
    • Triggerless read out
    – Many benchmark channels
    – Background & signal similar
    • Event Rate: 2 • 107/s
    3
    Raw Data Rate:
    200 GB/s
    Disk Storage Space for
    Offline Analysis: 3 PB/y
    Reduce by
    ~1/1000
    (Reject background events,
    save interesting physics events)

    View full-size slide

  5. Mitglied der Helmholtz-Gemeinschaft
    PANDA — Event Reconstruction
    • Triggerless read out
    – Many benchmark channels
    – Background & signal similar
    • Event Rate: 2 • 107/s
    3
    Raw Data Rate:
    200 GB/s
    Disk Storage Space for
    Offline Analysis: 3 PB/y
    Reduce by
    ~1/1000
    (Reject background events,
    save interesting physics events)
    GPUs

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  6. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  7. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  8. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  9. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  10. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  11. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  12. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  13. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  14. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  15. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 4
    Trigger
    Detector layers
    Usual HEP experiment
    PANDA
    PANDA — Tracking, Online Tracking
    • PANDA: No
    hardware-based
    trigger
    • But computational
    intensive software
    trigger
    → Online Tracking

    View full-size slide

  16. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    GPUs @ PANDA — Online Tracking
    • Port tracking algorithms to GPU
    – Serial → parallel
    – C++ → CUDA
    • Investigate suitability for online performance
    • But also: Find & invent tracking algorithms…
    • Under investigation:
    – Hough Transformation
    – Riemann Track Finder
    – Triplet Finder
    5

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  17. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Algorithm: Hough Transform
    • Idea: Transform (x,y)i → (α,r)ij, find lines via (α,r) space
    • Solve rij line equation for
    – Lots of hits (x,y,ρ)i
    and
    – Many αj ∈ [0°,360°) each
    • Fill histogram
    • Extract track parameters
    6
    x
    y
    x
    y
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Princip
    → Bin
    giv
    r
    α

    View full-size slide

  18. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Algorithm: Hough Transform
    • Idea: Transform (x,y)i → (α,r)ij, find lines via (α,r) space
    • Solve rij line equation for
    – Lots of hits (x,y,ρ)i
    and
    – Many αj ∈ [0°,360°) each
    • Fill histogram
    • Extract track parameters
    6
    rij =
    cos
    ↵j
    ·
    xi +
    sin
    ↵j
    ·
    yi + ⇢i
    i: ~100 hits/event (STT)
    j: every 0.2° rij: 180 000
    x
    y
    x
    y
    Mitglied der Helmholtz-Gemeinschaft
    Hough Transform — Princip
    → Bin
    giv
    r
    α

    View full-size slide

  19. °
    Angle /
    0 20 40 60 80 100 120 140 160 180
    Hough transformed
    -0.4
    -0.3
    -0.2
    -0.1
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6 0
    Entries 2.2356e+08
    Mean x 90
    Mean y 0.02905
    RMS x 51.96
    RMS y 0.1063
    0
    5
    10
    15
    20
    25
    0
    Entries 2.2356e+08
    Mean x 90
    Mean y 0.02905
    RMS x 51.96
    RMS y 0.1063
    1800 x 1800 Grid
    PANDA STT+MVD
    Mitglied der Helmholtz-Gemeinschaft
    7
    68 (x,y) points
    r
    α
    Algorithm: Hough Transform

    View full-size slide

  20. °
    Angle /
    0 20 40 60 80 100 120 140 160 180
    Hough transformed
    -0.4
    -0.3
    -0.2
    -0.1
    0
    0.1
    0.2
    0.3
    0.4
    0.5
    0.6 0
    Entries 2.2356e+08
    Mean x 90
    Mean y 0.02905
    RMS x 51.96
    RMS y 0.1063
    0
    5
    10
    15
    20
    25
    0
    Entries 2.2356e+08
    Mean x 90
    Mean y 0.02905
    RMS x 51.96
    RMS y 0.1063
    1800 x 1800 Grid
    PANDA STT+MVD
    Mitglied der Helmholtz-Gemeinschaft
    7
    68 (x,y) points
    r
    α
    Algorithm: Hough Transform

    View full-size slide

  21. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Algorithm: Hough Transform
    8
    Thrust Plain CUDA
    • Performance: 3 ms/event
    – Independent of α granularity
    – Reduced to set of standard routines
    • Fast (uses Thrust‘s optimized algorithms)
    • Inflexible (has it‘s limits, hard to customize)
    – No peakfinding included
    • Even possible?
    • Adds to time!
    • Performance: 0.5 ms/event
    – Built completely for this task
    • Fitting to every problem
    • Customizable
    • A bit more complicated at parts
    – Simple peakfinder implemented
    (threshold)
    • Using: Dynamic Parallelism, Shared
    Memory
    Two Implementations

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  22. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 9
    • Idea: Don‘t fit lines (in 2D), fit planes (in 3D)!
    • Create seeds
    – All possible three hit combinations
    • Grow seeds to tracks
    Continuously test next hit if it fits
    – Use mapping to Riemann paraboloid
    • Summer student project (J. Timcheck)
    x
    x
    x
    x
    y
    z‘
    x
    x
    x
    y
    x
    x
    x
    x
    y
    x
    Algorithm: Riemann Track Finder

    View full-size slide

  23. nLayerx
    = 1
    2
    ⇣p
    8x
    +
    1 1

    pos
    (
    nLayerx
    ) =
    3
    pp
    3
    p
    243x2 1
    +
    27x
    32
    /
    3
    + 1
    3
    p
    3
    3
    pp
    3
    p
    243x2 1
    +
    27x
    1
    Mitglied der Helmholtz-Gemeinschaft
    10
    Algorithm: Riemann Track Finder
    int ijk = threadIdx.x + blockIdx.x * blockDim.x;
    for () {for () {for () {}}}
    • GPU Optimization: Unfolding loops
    → 100 × faster than CPU version
    • Time for one event (Tesla K20X): ~0.6 ms

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  24. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 11
    Algorithm: Triplet Finder
    • Idea: Use only sub-set of detector as seed
    – Combine 3 hits to Triplet
    – Calculate circle from 3 Triplets (no fit)
    • Features
    – Tailored for PANDA
    – Fast & robust algorithm, no t0
    • Ported to GPU together with NVIDIA Application Lab

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  25. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 12
    Triplet Finder — Time

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  26. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamp
    – Combine hits to sets (bunches) which fill up GPU best
    13

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  27. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamp
    – Combine hits to sets (bunches) which fill up GPU best
    13
    Hit

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  28. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamp
    – Combine hits to sets (bunches) which fill up GPU best
    13
    Hit Event

    View full-size slide

  29. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamp
    – Combine hits to sets (bunches) which fill up GPU best
    13
    Hit Event

    View full-size slide

  30. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamp
    – Combine hits to sets (bunches) which fill up GPU best
    13
    Hit Event
    Bunch

    View full-size slide

  31. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Triplet Finder — Optimizations
    • Bunching Wrapper
    – Hits from one event have similar timestamp
    – Combine hits to sets (bunches) which fill up GPU best
    13
    Hit Event
    Bunch
    (N2) → (N)

    View full-size slide

  32. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 14
    Triplet Finder — Bunching
    Performance

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  33. Dynamic
    Parallelism
    Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Triplet Finder — Optimizations
    • Compare kernel launch strategies
    15
    1 thread/bunch
    Calling
    kernel
    1 thread/bunch
    Calling
    kernel
    Triplet
    Finder
    1 thread/bunch
    Calling
    kernel
    1 block/bunch
    Joined
    kernel
    1 block/bunch
    Joined
    kernel
    1 block/bunch
    Joined
    kernel
    TF Stage #1
    TF Stage #2
    TF Stage #3
    TF Stage #4
    1 stream/bunch
    Combining
    stream
    1 stream/bunch
    Combining
    stream
    1 stream/bunch
    Calling
    stream
    Joined
    Kernel
    Host
    Streams
    Triplet
    Finder
    Triplet
    Finder
    CPU
    GPU
    TF Stage #1
    TF Stage #2
    TF Stage #3
    TF Stage #4
    TF Stage #1
    TF Stage #2
    TF Stage #3
    TF Stage #4

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  34. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 16
    Triplet Finder — Kernel Launches
    Preliminary
    (in publication)

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  35. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2 17
    Triplet Finder — Clock Speed / Chipset
    Preliminary
    (in publication)
    K40 3004 MHz, 745 MHz / 875 MHz
    K20X 2600 MHz, 732 MHz / 784 MHz
    Memory Clock Core Clock GPU Boost

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  36. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Summary
    • Investigated different tracking algorithms
    – Best performance: 20 µs/event
    → Online Tracking a feasible technique for PANDA
    • Multi GPU system needed – (100) GPUs
    • Still much optimization necessary (efficiency)
    • Collaboration with NVIDIA Application Lab
    18

    View full-size slide

  37. Mitglied der Helmholtz-Gemeinschaft
    Andreas Herten, DPG Frühjahrstagung 2014, HK 57.2
    Summary
    • Investigated different tracking algorithms
    – Best performance: 20 µs/event
    → Online Tracking a feasible technique for PANDA
    • Multi GPU system needed – (100) GPUs
    • Still much optimization necessary (efficiency)
    • Collaboration with NVIDIA Application Lab
    18
    Thank you!
    Andreas Herten
    [email protected]

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