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Homework 9: Accelerating 1D convolution with threads

How to submit

Put all the code of inside hw.jl. Zip only this file (not its parent folder) and upload it to BRUTE. You should not not import anything but Base.Threads or just Threads.

Homework (2 points)

Implement multithreaded discrete 1D convolution operator[1] without padding (output will be shorter). The required function signature: thread_conv1d(x, w), where x is the signal array and w the kernel. For testing correctness of the implementation you can use the following example of a step function and it's derivative realized by kernel [-1, 1]:

using Test
@test all(thread_conv1d(vcat([0.0, 0.0, 1.0, 1.0, 0.0, 0.0]), [-1.0, 1.0]) .≈ [0.0, -1.0, 0.0, 1.0, 0.0])

Your parallel implementation will be tested both in sequential and two threaded mode with the following inputs

using Random
Random.seed!(42)
x = rand(10_000_000)
w = [1.0, 2.0, 4.0, 2.0, 1.0]
@btime thread_conv1d($x, $w);

On your local machine you should be able to achieve 0.6x reduction in execution time with two threads, however the automatic eval system is a noisy environment and therefore we require only 0.8x reduction therein. This being said, please reach out to us, if you encounter any issues.

HINTS:

  • start with single threaded implementation
  • don't forget to reverse the kernel
  • @threads macro should be all you need
  • for testing purposes create a simple script, that you can run with julia -t 1 and julia -t 2