Complete Benchmark Codes, Perform Benchmark Tests, and Report Results

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Issue Description

1. Complete Benchmark Codes

I propose completing the benchmark codes for the project to assess and compare the performance of various functionalities. The benchmark codes should cover critical areas of the codebase and be designed to measure the execution time, memory usage, or any other relevant metrics.

• Identify critical areas for benchmarking
• Add benchmark codes to measure performance
• Ensure benchmark codes are well-documented

2. Perform Benchmark Tests

Execute the completed benchmark codes and collect data to assess the project's performance. It's crucial to run the benchmark tests under various scenarios or configurations to capture a comprehensive understanding of the project's performance characteristics.

• Run benchmark tests on different hardware configurations (if applicable)
• Vary input data or parameters to assess performance under different conditions
• Document the testing environment and configurations used

3. Report Results

Create a comprehensive report summarizing the results of the benchmark tests. The report should include:

• Execution time for critical functionalities
• Memory usage patterns and benchmarks
• Comparative analysis with previous benchmark results (if available)
• Any identified performance bottlenecks or areas for improvement