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Project 2 Stream Compaction Instructions

This is due Tuesday, September 21 2021 at midnight.

Summary: In this project, you'll implement GPU stream compaction in CUDA, from scratch. This algorithm is widely used, and will be important for accelerating your path tracer project.

Your stream compaction implementations in this project will simply remove 0s from an array of ints. In the path tracer, you will remove terminated paths from an array of rays.

In addition to being useful for your path tracer, this project is meant to reorient your algorithmic thinking to the way of the GPU. On GPUs, many algorithms can benefit from massive parallelism and, in particular, data parallelism: executing the same code many times simultaneously with different data.

You'll implement a few different versions of the Scan (Prefix Sum) algorithm. First, you'll implement a CPU version of the algorithm to reinforce your understanding. Then, you'll write a few GPU implementations: "naive" and "work-efficient." Finally, you'll use some of these to implement GPU stream compaction.

Algorithm overview & details: There are two primary references for details on the implementation of scan and stream compaction.

Your GPU stream compaction implementation will live inside of the stream_compaction subproject. In this way, you will be able to easily copy it over for use in your GPU path tracer.

Part 0: The Usual

This project (and all other CUDA projects in this course) requires an NVIDIA graphics card with CUDA capability. Any card with Compute Capability 2.0 (sm_20) or greater will work. Check your GPU on this compatibility table. If you do not have a personal machine with these specs, you may use the CETS computers in Moore 100 or the SIG Lab which have supported GPUs.

Useful existing code

  • stream_compaction/common.h
    • checkCUDAError macro: checks for CUDA errors and exits if there were any.
    • ilog2ceil(x): computes the ceiling of log2(x), as an integer.
  • main.cpp
    • Some testing code for your implementations.

Note 1: The tests will simply compare against your CPU implementation Do it first!

Note 2: The tests default to an array of size 256. Test with something larger (10,000? 1,000,000?), too!

Part 1: CPU Scan & Stream Compaction

This stream compaction method will remove 0s from an array of ints.

Do this first, and double check the output! It will be used as the expected value for the other tests.

In stream_compaction/cpu.cu, implement:

  • StreamCompaction::CPU::scan: compute an exclusive prefix sum. For performance comparison, this is supposed to be a simple for loop. But for better understanding before starting moving to GPU, you can simulate the GPU scan in this function first.
  • StreamCompaction::CPU::compactWithoutScan: stream compaction without using the scan function.
  • StreamCompaction::CPU::compactWithScan: stream compaction using the scan function. Map the input array to an array of 0s and 1s, scan it, and use scatter to produce the output. You will need a CPU scatter implementation for this (see slides or GPU Gems chapter for an explanation).

These implementations should only be a few lines long.

Part 2: Naive GPU Scan Algorithm

In stream_compaction/naive.cu, implement StreamCompaction::Naive::scan

This uses the "Naive" algorithm from GPU Gems 3, Section 39.2.1. Example 39-1 uses shared memory. This is not required in this project. You can simply use global memory. As a result of this, you will have to do ilog2ceil(n) separate kernel invocations.

Since your individual GPU threads are not guaranteed to run simultaneously, you can't generally operate on an array in-place on the GPU; it will cause race conditions. Instead, create two device arrays. Swap them at each iteration: read from A and write to B, read from B and write to A, and so on.

Beware of errors in Example 39-1 in the chapter; both the pseudocode and the CUDA code in the online version of Chapter 39 are known to have a few small errors (in superscripting, missing braces, bad indentation, etc.)

Be sure to test non-power-of-two-sized arrays.

Part 3: Work-Efficient GPU Scan & Stream Compaction

3.1. Scan

In stream_compaction/efficient.cu, implement StreamCompaction::Efficient::scan

Most of the text in Part 2 applies.

  • This uses the "Work-Efficient" algorithm from GPU Gems 3, Section 39.2.2.
  • This can be done in place - it doesn't suffer from the race conditions of the naive method, since there won't be a case where one thread writes to and another thread reads from the same location in the array.
  • Beware of errors in Example 39-2.
  • Test non-power-of-two-sized arrays.

Since the work-efficient scan operates on a binary tree structure, it works best with arrays with power-of-two length. Make sure your implementation works on non-power-of-two sized arrays (see ilog2ceil). This requires extra memory

  • your intermediate array sizes will need to be rounded to the next power of two.

3.2. Stream Compaction

This stream compaction method will remove 0s from an array of ints.

In stream_compaction/efficient.cu, implement StreamCompaction::Efficient::compact

For compaction, you will also need to implement the scatter algorithm presented in the slides and the GPU Gems chapter.

In stream_compaction/common.cu, implement these for use in compact:

  • StreamCompaction::Common::kernMapToBoolean
  • StreamCompaction::Common::kernScatter

Part 4: Using Thrust's Implementation

In stream_compaction/thrust.cu, implement:

  • StreamCompaction::Thrust::scan

This should be a very short function which wraps a call to the Thrust library function thrust::exclusive_scan(first, last, result).

To measure timing, be sure to exclude memory operations by passing exclusive_scan a thrust::device_vector (which is already allocated on the GPU). You can create a thrust::device_vector by creating a thrust::host_vector from the given pointer, then casting it.

For thrust stream compaction, take a look at thrust::remove_if. It's not required to analyze thrust::remove_if but you're encouraged to do so.

Part 5: Why is My GPU Approach So Slow? (Extra Credit) (+5)

If you implement your efficient scan version following the slides closely, there's a good chance that you are getting an "efficient" gpu scan that is actually not that efficient -- it is slower than the cpu approach?

Though it is totally acceptable for this assignment, In addition to explain the reason of this phenomena, you are encouraged to try to upgrade your work-efficient gpu scan.

Thinking about these may lead you to an aha moment:

  • What is the occupancy at a deeper level in the upper/down sweep? Are most threads actually working?
  • Are you always launching the same number of blocks throughout each level of the upper/down sweep?
  • If some threads are being lazy, can we do an early termination on them?
  • How can I compact the threads? What should I modify to keep the remaining threads still working correctly?

Keep in mind this optimization won't need you change a lot of your code structures. It's all about some index calculation hacks.

If you don't run into the slower gpu approach. Congratulations! You are way ahead and you earn this extra credit automatically.

Part 6: Radix Sort (Extra Credit) (+10)

Add an additional module to the stream_compaction subproject. Implement radix sort using one of your scan implementations. Add tests to check its correctness.

Part 7: GPU Scan Using Shared Memory && Hardware Optimization(Extra Credit) (+10)

Implement GPU Gem Ch 39 Example 39.1, 39.2.

Notice that the size of the shared memory is dynamic and related to the block size. Since each SM has limited shared memory, the block size you set will affect the occupancy of the blocks in each SM. For example, let's say your graphics card has N Kb of shared memory per SM, if you use the maximum of N Kb shared memory per block, then you would have a max occupancy of 1 block per SM. This might not be the best performance.

Besides we can optimize the efficiency by changing our memory access pattern to avoid bank conflicts. See GPU Gem Ch 39 Section 39.2.3. This hasn't been covered in the course but we encourage you to challenge yourself.

Write-up

  1. Update all of the TODOs at the top of your README.md.
  2. Add a description of this project including a list of its features.
  3. Add your performance analysis (see below).

All extra credit features must be documented in your README.md, explaining its value (with performance comparison, if applicable!) and showing an example how it works. For radix sort, show how it is called and an example of its output.

Always profile with Release mode builds and run without debugging.

Questions

  • Roughly optimize the block sizes of each of your implementations for minimal run time on your GPU.

    • (You shouldn't compare unoptimized implementations to each other!)

  • Compare all of these GPU Scan implementations (Naive, Work-Efficient, and Thrust) to the serial CPU version of Scan. Plot a graph of the comparison (with array size on the independent axis).

    • We wrapped up both CPU and GPU timing functions as a performance timer class for you to conveniently measure the time cost.
      • We use std::chrono to provide CPU high-precision timing and CUDA event to measure the CUDA performance.
      • For CPU, put your CPU code between timer().startCpuTimer() and timer().endCpuTimer().
      • For GPU, put your CUDA code between timer().startGpuTimer() and timer().endGpuTimer(). Be sure not to include any initial/final memory operations (cudaMalloc, cudaMemcpy) in your performance measurements, for comparability.
      • Don't mix up CpuTimer and GpuTimer.
    • To guess at what might be happening inside the Thrust implementation (e.g. allocation, memory copy), take a look at the Nsight timeline for its execution. Your analysis here doesn't have to be detailed, since you aren't even looking at the code for the implementation.

  • Write a brief explanation of the phenomena you see here.

    • Can you find the performance bottlenecks? Is it memory I/O? Computation? Is it different for each implementation?

  • Paste the output of the test program into a triple-backtick block in your README.

    • If you add your own tests (e.g. for radix sort or to test additional corner cases), be sure to mention it explicitly.

These questions should help guide you in performance analysis on future assignments, as well.

Submit

If you have modified any of the CMakeLists.txt files at all (aside from the list of SOURCE_FILES), mentions it explicity. Beware of any build issues discussed on the Google Group.

Open a GitHub pull request so that we can see that you have finished. The title should be "Project 2: YOUR NAME". The template of the comment section of your pull request is attached below, you can do some copy and paste:

  • Repo Link
  • (Briefly) Mentions features that you've completed. Especially those bells and whistles you want to highlight
    • Feature 0
    • Feature 1
    • ...
  • Feedback on the project itself, if any.

GPU Gem 3 Ch 39 Patch

  • Example 1

  • Example 2

  • Figure-39-4

  • Figure-39-2. This image shows an naive inclusive scan. We should convert this to an exclusive one for compaction.

Algorithm Examples

  • scan:
    • goal: produce a prefix sum array of a given array (we only care about exclusive scan here)
    • input
      • [1 5 0 1 2 0 3]
    • output
      • [0 1 6 6 7 9 9]
  • compact:
    • goal: closely and neatly packed the elements != 0
    • input
      • [1 5 0 1 2 0 3]
    • output
      • [1 5 1 2 3]
  • compactWithoutScan (CPU)
    • an implementation of compact. So the goal, input and output should all be the same as compact
    • Simply loop through the input array, meanwhile maintain a pointer indicating which address shall we put the next non-zero element
  • compactWithScan (CPU/GPU)
    • an implementation of compact. So the goal, input and output should all be the same as compact
    • 3 steps
      • map
        • goal: map our original data array (integer, Light Ray, etc) to a bool array
        • input
          • [1 5 0 1 2 0 3]
        • output
          • [1 1 0 1 1 0 1]
      • scan
        • take the output of last step as input
        • input
          • [1 1 0 1 1 0 1]
        • output
          • [0 1 2 2 3 4 4]
      • scatter
        • preserve non-zero elements and compact them into a new array
        • input:
          • original array
            • [1 5 0 1 2 0 3]
          • mapped array
            • [1 1 0 1 1 0 1]
          • scanned array
            • [0 1 2 2 3 4 4]
        • output:
          • [1 5 1 2 3]
        • This can be done in parallel on GPU
        • You can try multi-threading on CPU if you want (not required and not our focus)
        • for each element input[i] in original array
          • if it's non-zero (given by mapped array)
          • then put it at output[index], where index = scanned[i]