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massCorrelation

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An exercise in writing an efficient correlation calculator

Overview

This is primarly an exercise in implementing a correlation calculation,

The primary implementation is already quite fast but I wanted to know how fast could I get, In chronological order :

  • Baseline algo came from the R project with some optimisation for repated paring of vectors.
  • Matrix Algorithm was describe in a stackoverflow post
  • CUDA Implementation of both algorithm
  • Multithreading implementation with pthread and OpenMP

This program is very easy to parallelize due to no depency from one result to another, resulting in very little need for synchronization between threads (The only synchronization needed was to manage the task queue between the different threads in a 1-producer n-consumer ).

We are of course assuming :

  • That there is enough memory to hold in memory both the input and the result data.
  • Data type used for calculation is float.
  • Multi-thread code do not make any effort toward the processor and use a threadpool of 128 threads.
  • Measured timing highly depend on I/O right now. Will attempt to reduce that dependency in the future.

Measured Timing

Time have been measured on an Intel E5606 CUDA code is run on one Tesla C2075

input : 601 x 45101 matrix

  • Baseline Implementation : 977.89
  • CUDA : 98.27
  • Matrix Implementation : 1008.80
  • Matrix CUDA : 142.23
  • Multi-threaded : 305.19
  • openMP : 475.90 (to be checked later when the node is less loaded )
  • openMP Nested : 349.13
  • No calculation : 56.64

for comparison on an Intel X5690

  • Baseline Implementation : 640.27
  • Matrix Implementation : 639.95
  • Multi-threaded : 82.10
  • openMP : 130.34
  • openMP Nested : 115.11
  • No calculation : 9.80

input : 100 x 10000 (generated with randomMatrix.pl)

Intel E5606

  • Baseline : 11.40 (9.08)
  • CUDA : Unavailable at this time
  • Matrix : 11.18 (8.80)
  • Matrix CUDA : Unavailable at this time
  • Multi-threaded : 7.39 (5.22)
  • OpenMP : 6.26 (3.99)
  • OpenMP Nested : 6.04 (3.71)
  • No calculation : 2.63 (0.33)

Intel X5690

  • Baseline : 5.67 (5.45)
  • CUDA : 3.27 (1.12)
  • Matrix : 5.53 (5.23)
  • Matrix CUDA : 3.21 (1.13)
  • Multi-threaded : 0.94 (0.72)
  • openMP : 1.25 (1.03)
  • OpenMP Nested : 2.97 (2.74)
  • No calculation : 0.43 (0.22)

Timing on Tegra2 T20

  • Baseline : 124.26 (78.09)
  • Matrix : 119.02 (76.48)
  • Thread : 75.11 (41.43)
  • OpenMP : 95.44 (61.21)
  • OpenMP nested : 93.57 (56.98)
  • No calculation :47.44 (2.44)

Notes

The CUDA implementation have been quite straight-forward to implement and provided benefits out of the box, Attempt to cleverly optimize the CUDA kernel by using shared memory were unsuccessful ( no performance gained ), and trade-offs were unacceptable ( reducing the number of thread to accomodate the size of the shared memory ). While the multi-thread code required some implementation for the threadpool, and might be optimized further by using more specialized queues (which could reduce the time used in allocation ).