# FFT Benchmark Implementation Summary

## Overview

This document summarizes the comprehensive benchmarking suite implemented for the `scirs2-fft` module. The benchmarks cover performance, memory usage, and numerical accuracy across a wide range of FFT operations.

## Implemented Benchmarks

### 1. Performance Benchmarks (`fft_benchmarks.rs`)

The core performance benchmarks measure execution time using Criterion:

- **1D FFT Operations**: FFT, RFFT, IFFT, IRFFT
- **2D FFT Operations**: FFT2, FFTN
- **Fractional Fourier Transform**: Multiple alpha orders
- **Memory-Efficient Operations**: In-place FFT, optimized 2D FFT

These benchmarks measure throughput and latency for various input sizes and provide a baseline for performance tracking.

### 2. SciPy Comparison (`scipy_comparison.rs`)

Direct comparison with SciPy's FFT implementation:

- **Enhanced 1D FFT Benchmarks**: Comprehensive size and operation testing
- **Multi-dimensional FFT**: 2D and N-D transforms
- **Specialized Transforms**: DCT, DST, FrFT
- **Worker Scaling**: Tests parallel scaling behavior

Includes a comparison script generator for Python benchmark execution.

### 3. Memory Profiling (`memory_profiling.rs`)

Custom memory usage tracking:

- **Allocation Tracking**: Measures number and size of allocations
- **Peak Memory Usage**: Maximum memory used during operation
- **Allocation Patterns**: When and how memory is allocated

Uses a custom allocator wrapper to intercept and measure allocations.

### 4. Accuracy Comparison (`accuracy_comparison.rs`)

Thorough numerical accuracy testing:

- **Analytical Accuracy**: Tests against known transforms
- **Energy Conservation**: Verifies Parseval's theorem
- **Inverse Accuracy**: Forward-inverse transform error
- **Transform Properties**: Tests additivity and other mathematical properties

Includes configurable tolerance thresholds and detailed error metrics.

### 5. Visual Analysis (`benchmark_analysis.rs`)

Graphical representation of benchmark results:

- **Performance Plots**: Time vs. input size
- **Memory Usage Graphs**: Memory consumption patterns
- **Accuracy Charts**: Error metrics visualization
- **Comparison Tables**: Tabular data for detailed examination

Uses Plotly for interactive HTML visualizations.

## Benchmark Runner

A comprehensive script (`run_all_benchmarks.sh`) executes all benchmarks in sequence:

1. Runs Rust performance benchmarks
2. Profiles memory usage
3. Tests numerical accuracy
4. Compares with SciPy (if available)
5. Generates summary reports

## Benchmarking Guide

A detailed guide (`BENCHMARKING_GUIDE.md`) explains:

- How to run individual benchmarks
- How to interpret results
- Performance optimization tips
- Configuration options
- Troubleshooting advice

## Key Metrics

The benchmark suite reports several key metrics:

| Metric | Description | Implementation |
|--------|-------------|----------------|
| Execution Time | Time taken for operation | Criterion measurements |
| Throughput | Operations per second | Criterion benchmarks |
| Peak Memory | Maximum memory allocation | Custom allocator tracking |
| Allocation Count | Number of memory allocations | Custom allocator tracking |
| Max Error | Largest deviation from expected | Analytical comparisons |
| Mean Error | Average deviation | Statistical calculations |
| RMS Error | Root mean square error | Statistical calculations |
| Relative Error | Error relative to signal magnitude | Mathematical computation |

## Performance Targets

The benchmarks establish the following performance targets:

1. **1D FFT**: < 1ms for 4096 points
2. **2D FFT**: < 10ms for 256x256
3. **Memory overhead**: < 2x input size
4. **Accuracy**: < 1e-10 relative error

## Future Enhancements

Planned benchmark extensions:

1. **Hardware-specific optimization analysis**
2. **SIMD acceleration comparison**
3. **GPU performance comparison**
4. **Cross-platform benchmark comparisons**
5. **CI integration for continuous performance tracking**

## Conclusion

The implemented benchmarking suite provides comprehensive tools for evaluating and optimizing the performance, memory usage, and accuracy of the `scirs2-fft` module. It establishes a solid baseline for comparing against established libraries like SciPy and for tracking improvements in future development.