Blelloch Scan - Intro to Parallel Programming

Udacity
23 Feb 201504:29
EducationalLearning
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TLDRThe transcript discusses an efficient algorithm for performing an exclusive scan on a sequence, which involves a two-stage process: reduction and downsweep. The reduction stage aggregates values in a hierarchical manner, while the downsweep stage uses a different operator to compute the final results. The method is exemplified with an exclusive sum scan, and the output sequence reflects the cumulative sum up to each point. The transcript concludes with a quiz to compute a max exclusive scan using the same method.

Takeaways
  • 🚀 Hillis and Steele scan is an efficient parallel algorithm, being one of the first to be implemented on GPUs.
  • 🌟 Guy Blelloch's formulation of scan from 1990 is noted for its improved work efficiency, despite being more complex algorithmically.
  • 🔄 The algorithm consists of two main stages: reduction and downsweep, which are part of an exclusive scan operation.
  • 📈 An example exclusive sum scan is performed on the input array from 1 to 8, illustrating the two-stage process.
  • 🔢 The reduction stage involves adding neighbors at increasing hop distances and retaining intermediate results for later use.
  • 🔄 The downsweep stage starts by resetting the rightmost data to the identity operator's value and then mirrors the reduction pattern.
  • 📊 During downsweep, each operator takes two inputs and produces two outputs, utilizing the intermediate results from the reduction stage as necessary.
  • 🔎 The output sequence from the downsweep reflects the cumulative sum of all preceding elements, exemplified by the output 21 being the sum of 1 to 6.
  • 💡 The script concludes with a quiz to compute the max exclusive scan for a given input sequence using the described reduction-downsweep method.
  • 📝 The final output should encapsulate the key points of the script, providing a clear and concise summary of the main concepts and procedures.
Q & A

  • What is the Hillis and Steele scan?

    -The Hillis and Steele scan is an efficient algorithm that was one of the first to be implemented on GPUs for parallel computation.

  • Who popularized another formulation of the scan?

    -Guy Blelloch popularized another formulation of the scan in 1990, which is known for its improved work efficiency.

  • What are the two stages of the Blelloch scan?

    -The Blelloch scan consists of two stages: the reduction stage and the downsweep stage.

  • What type of scan is performed on the input array 1 through 8?

    -An exclusive sum scan is performed on the input array from 1 to 8.

  • How does the reduction stage work in the Blelloch scan?

    -The reduction stage adds neighbors at increasing hop distances (1, 2, and 4 hops away) and retains intermediate results for use in the downsweep stage.

  • What is the purpose of the downsweep stage in the Blelloch scan?

    -The downsweep stage uses a mirror image communication pattern of the reduction stage but with a different operator, producing two outputs instead of one.

  • What are the two differences in the downsweep stage compared to the reduction stage?

    -In the downsweep stage, a different operator is used, and it produces two outputs instead of one, utilizing the intermediate results from the reduction stage.

  • What is the output sequence of the exclusive sum scan for the input vector from 1 to 8?

    -The output sequence of the exclusive sum scan is 0, 1, 3, 6, 10, 15, 21, 28.

  • How does the output sequence represent the exclusive sum scan?

    -Each output in the sequence is the sum of all elements before it in the input vector, excluding the current element.

  • What is the identity operator for the sum scan?

    -The identity operator for the sum scan is 0, as it represents the starting value for the accumulation.

  • How can you compute the max exclusive scan of the input sequence 2 1 4 3 using the reduced downsweep method?

    -You would perform a reduction to find local maxima and then a downsweep to combine these maxima while excluding the current element from the sum, using the intermediate results from the reduction stage.

Outlines
00:00
🚀 Introduction to Efficient Scan Algorithms

This paragraph introduces the efficiency of the Hillis and Steele scan algorithm, the first to be implemented on GPUs. It contrasts this with Guy Blelloch's more efficient formulation from 1990, which is slightly more complex. The paragraph focuses on an exclusive sum scan of the input array from 1 to 8, detailing the two-stage process of reduction followed by downsweep. The explanation highlights the use of intermediate results in the reduction stage and the mirrored communication pattern in the downsweep stage, which involves a different operator and the utilization of intermediate results to fill in missing data.

Mindmap
Keywords
💡Hillis and Steele scan
The Hillis and Steele scan is an algorithm for parallel computation that is known for its efficiency, particularly in the context of GPU (Graphics Processing Unit) implementations. It is foundational to understanding more complex scan algorithms discussed in the video. In the script, it is mentioned as the first scan to be implemented on GPUs, highlighting its significance in the evolution of parallel computing.
💡GPU
GPU stands for Graphics Processing Unit, a specialized electronic circuit designed to rapidly manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display device. In the context of the video, GPUs are noted for their ability to efficiently execute the Hillis and Steele scan algorithm, indicating their utility in parallel processing tasks.
💡Guy Blelloch
Guy Blelloch is a computer scientist known for his work in parallel algorithms and their implementation. In the video, he is credited with popularizing another formulation of the scan algorithm in 1990, which is suggested to be more efficient in terms of work than the Hillis and Steele scan, although it is more complex algorithmically.
💡Scan algorithm
A scan algorithm is a parallel computing algorithm used to perform prefix computations, such as cumulative sums or products, on an array of data. The video focuses on the efficiency and implementation of different scan algorithms, including the Hillis and Steele scan and the more complex formulation popularized by Guy Blelloch.
💡Work efficiency
Work efficiency in the context of the video refers to the effectiveness with which an algorithm uses computational resources to perform a task. An algorithm that is more work-efficient requires fewer resources or completes the task more quickly. The video discusses the work efficiency of different scan algorithms, comparing the Hillis and Steele scan with Guy Blelloch's formulation.
💡Reduction
In the context of the video, reduction refers to the first stage of the scan algorithm, where elements of the input array are combined to produce intermediate results. This process involves iteratively combining neighboring elements, starting with immediate neighbors and increasing the distance with each step.
💡Downsweep
Downsweep is the second stage of the scan algorithm discussed in the video, following the reduction stage. It involves a process that 'sweeps' through the intermediate results obtained during reduction, using a different operator to combine them in a manner that is the mirror image of the reduction process. This stage is unique in that it produces two outputs for each pair of inputs, utilizing the intermediate results from the reduction stage.
💡Exclusive scan
An exclusive scan is a type of scan operation that does not include the current element in the cumulative computation. It is used to create a prefix sum where each element of the output array is the sum of all elements to the left of the current position in the input array. The video provides an example of performing an exclusive sum scan on the input array 1 through 8.
💡Intermediate results
Intermediate results in the context of the scan algorithm refer to the partial outcomes that are produced during the reduction stage and are used later in the downsweep stage. These results are essential for the correct computation of the final output sequence in an exclusive scan.
💡Identity operator
The identity operator is a function that, when applied to any element, returns the element unchanged. In the context of the exclusive sum scan discussed in the video, the identity operator for the sum operation is 0, as adding 0 to any number does not change the value of that number.
💡Max scan
A max scan is a variant of the scan algorithm where the goal is to find the maximum value in a subsequence of the input array rather than performing a cumulative sum or product. The video poses a quiz to compute the max scan of a given input sequence using the reduced downsweep method.
Highlights

Hillis and Steele scan is an efficient algorithm, being the first to be implemented on GPUs.

Guy Blelloch popularized a more work-efficient formulation of scan in 1990.

The algorithm operates in two stages: reduction and downsweep.

The discussed scan is an exclusive sum scan on the input array from 1 to 8.

The reduction stage involves adding neighbors at increasing hop distances and keeping intermediate results.

The downsweep stage is a mirror image of the reduction but uses a different operator.

During downsweep, a different operator is used that produces two outputs instead of one.

Intermediate results are utilized during the downsweep to fill in missing data.

The output sequence of the exclusive sum scan is 0, 1, 3, 6, 10, 15, 21, 28.

Each output represents the sum of all elements before it in the input sequence.

The algorithm results in an exclusive max scan when applied to the input sequence 2, 1, 4, 3.

The quiz involves computing the max scan using the same reduction and downsweep method.

The process starts with a reduction phase, followed by a downsweep phase to complete the scan.

The scan algorithm is innovative in its use of intermediate results and a two-stage process.

The method's complexity lies in the algorithm's details, particularly in the downsweep stage.

The algorithm's efficiency is highlighted by its implementation on GPUs and work efficiency.

The exclusive scan provides a sum that excludes the current element, offering a different perspective on data.

The practical application of this algorithm can be seen in parallel computing and efficient data processing.

Transcripts

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GPU-AlgorithmsScan-TechniquesBlelloch-FormulationExclusive-ScanReduction-StageDownsweep-StageAlgorithm-ComplexitySum-ScanIntermediate-ResultsMax-Scan-Quiz