How Can SSE SIMD Instructions Accelerate Parallel Prefix Sum Computation?

Parallelizing Prefix Sum with SSE SIMD

Implementing a parallel prefix sum algorithm is crucial for optimizing performance in various computational tasks. This article investigates a fast and efficient prefix sum approach using SIMD (Single Instruction Multiple Data) instructions found in Intel CPUs.

SSE SIMD Acceleration

To accelerate the prefix sum computation, we can leverage the power of SSE (Streaming SIMD Extensions). The first pass of the algorithm can be optimized by performing parallel partial sums using SSE on pairs of elements. This approach reduces the processing time.

Pass 2 Optimization

In the second pass, we aim to add the cumulative sum from the preceding partial sum to the current partial sum. Since a constant value is being added, we can further optimize this operation with SSE. This step improves the efficiency of the second pass.

Overall Performance

For an array of n elements and a SIMD width of w, the algorithm's time cost is approximately (n/m) * (1 1/w). With four cores and a SIMD width of four, the speedup over sequential code is about 5n/16, or approximately 3.2 times faster.

Special Case Optimization

In specific scenarios, it's possible to use SIMD on both the first and second passes. This further enhances performance, reducing the time cost to 2n/(mw).

Code Implementation

The provided code demonstrates the implementation of the parallel prefix sum algorithm with SSE optimization. The function scan_omp_SSEp2_SSEp1_chunk takes an array a and computes the cumulative sum, storing it in the array s.

This code provides a highly optimized implementation of the prefix sum algorithm, significantly improving performance for large arrays. The code includes optimizations for both the first and second passes, utilizing SSE instructions to accelerate the computation.

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