Design multithreaded 1D convolution strategies

Q: Design multithreaded 1D convolution strategies

This question evaluates competency in parallel programming, CPU performance optimization, cache locality, load balancing, and synchronization for multithreaded numerical algorithms.

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Question

Optimize CPU Multithreaded 1D "Valid" Convolution

Context

You are given a 1D input array x of length N and a kernel h of length K. The "valid" convolution produces an output array y of length L_out = N − K + 1, where:

y[i] = sum_{j=0}^{K-1} x[i + j] * h[K − 1 − j]
Index i ranges from 0 to L_out − 1.

Assume a typical CPU with a shared last-level cache, private L1/L2 per core, 64-byte cache lines, and support for multiple threads.

Task

Optimize the valid 1D convolution for CPU hardware using multithreading. For each case, describe and implement (code or pseudocode) how to:

Partition work,
Assign threads,
Combine results,
Address load balancing, cache locality, and avoiding false sharing,
Synchronize/merge outputs,
Choose chunk sizes and the number of threads.

Consider these cases:

N = 1,000,000; K = 3,
N = 1,000,000; K = 1,000,000,
Maximum available threads = 100.

Design multithreaded 1D convolution strategies

Optimize CPU Multithreaded 1D "Valid" Convolution

Context

Task

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Design multithreaded 1D convolution strategies

Overview

Optimize CPU Multithreaded 1D "Valid" Convolution

Context

Task

Solution

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