Future Improvements

Prompt

Look at the instructions in the program DFT.py in the Project Knowledge area. Are we using all the features of the RP2350 SoC instruction set ARMv8-M + Thumb-2 and the Single-precision floating point unit (FPv5-SP)?

Claude Response

I examined the dft.py file, which contains ARM assembler code for FFT implementation. The code is not taking full advantage of the RP2350's ARMv8-M architecture and FPv5-SP floating-point capabilities.

Key observations:

The code is explicitly targeting ARMv7-M with Thumb instructions, as stated in the README.md: "Requires: ARM platform with FPU supporting Arm Thumb V7 assembler."
The code uses basic FPU operations like vldr, vstr, vadd, vsub, vmul, vdiv, etc., but doesn't utilize ARMv8-M specific enhancements or newer FPv5-SP features such as:
SIMD instructions (single instruction, multiple data)
Advanced vector operations available in newer ARM architectures
Hardware loop instructions available in ARMv8-M
Specialized DSP instructions

The author even acknowledges this in the README section "Future development": "Modern compilers mean that the traditional performance benefit of assembler is nonexistent unless the assembler code is hand crafted and optimised to an extreme level. This is because the compiler exploits details of the internal design of the CPU in ways which are difficult for the programmer to achieve."

The code was designed for compatibility across multiple platforms (Pyboard 1.x, Pyboard D, Pico 2), which likely led to the use of a more conservative instruction set that would work across all target devices. The code is functional but could potentially be optimized further to take advantage of the RP2350's more advanced instruction set, which might result in better performance for FFT operations.

Prompt

What changes to improve performance would you recommend we make in DFT.py to make it faster on the ARMv7-M with Thumb instruction with the Single-precision floating point unit (FPv5-SP)?

Based on my analysis of the dft.py code, here are specific optimizations to improve FFT performance on the RP2350 with ARMv7-M Thumb and FPv5-SP:

Use SIMD operations for vector processing:
Replace sequential floating-point operations with SIMD instructions where possible
For example, use vector load/store instructions to process multiple elements at once
Optimize memory access patterns:
Rearrange data structures to improve cache locality
Use pre-fetching instructions to reduce cache misses
Align data to cache line boundaries
Use pld (preload) instructions before accessing memory
Loop optimizations:
Unroll critical loops (especially in the DOMATHS and FFT butterfly sections)
Use fewer branches in tight loops to reduce branch prediction failures
Leverage FPv5-SP specific instructions:
Use fused multiply-add operations (vfma, vfms) instead of separate multiply and add
These instructions can complete in a single cycle on FPv5-SP
Register utilization improvements:
Keep more intermediate values in FPU registers to reduce load/store operations
The current implementation frequently moves values between memory and registers
Rework register allocation to minimize register spilling
Algorithm-specific optimizations:
Implement radix-4 or split-radix FFT instead of radix-2
Radix-4 requires 25% fewer complex multiplications than radix-2
Consider implementing a mixed-radix approach for non-power-of-2 lengths
Reduce function call overhead:
Inline small assembler functions like CADD, CSUB, and CMUL at their call sites
This eliminates the overhead of pushing/popping registers and branch instructions
Specialized scaling approach:
Defer scaling operations until the end of the transform
Apply scaling only where necessary, not to every element
Dual-issue optimization:
Rearrange instructions to improve dual-issue performance on the Cortex-M7
Interleave FPU and integer operations where possible
Reduce twiddle factor computation overhead:
- Precompute more twiddle factors
- Consider storing them in a more efficient format

These optimizations could significantly improve the FFT performance, potentially getting closer to the theoretical limits of the hardware. The most substantial gains would likely come from SIMD operations, better memory access patterns, and the use of fused multiply-add instructions.

Prompt

Of all these 10 possible changes, which ones would have the lowest risk of breaking the existing code that we could try. We would want to do timings on both versions to test to see if the changes improved the performance.

Looking at the possible optimizations, I'd recommend these lower-risk changes that could improve performance while minimizing the chance of breaking existing functionality:

Use fused multiply-add operations - Replacing separate multiply and add operations with vfma and vfms instructions is relatively straightforward and low-risk. For example, in the CMUL function, you could replace:

vmul(s10, s12, s14)     # s10 = ax
vmul(s9, s13, s15)      # s9  = by
vsub(s10, s10, s9)      # s10 = ax - by

with something like:

vmul(s10, s12, s14)     # s10 = ax
vneg(s9, s13)           # s9 = -ay (if needed)
vfms(s10, s13, s15)     # s10 = ax - (by)

Loop unrolling - Identify the most performance-critical loops (like the butterfly operations) and manually unroll them. This is a localized change that's unlikely to break functionality while reducing branch overhead.
Register utilization improvements - Reducing the number of loads and stores by keeping values in registers longer is relatively safe. Look for patterns where values are stored and then immediately reloaded.
Minimize function call overhead - The CMUL, CADD, and CSUB functions are called frequently during the transform. Inlining these at their call sites would eliminate function call overhead without changing their functionality.
Memory alignment improvements - Ensuring data is properly aligned for the FPU can improve performance without changing the algorithm. This might involve adjusting how arrays are allocated.

To properly test these changes:

Create a copy of the original code as a baseline
Implement each optimization separately
Run identical benchmarks on both versions
Measure both execution time and verify results match the original implementation

The benchmark should perform multiple FFT operations on the same data set to get a statistically significant measurement. If you have access to an oscilloscope, measuring the execution time with GPIO pins can provide more accurate timing than software methods.

Synthetic Data For Testing Performance

Prompt

Could we create synthetic data to test the new version of the FFT?

Response

Yes, creating synthetic data is an excellent approach for testing and validating FFT implementations. It provides predictable inputs with known expected outputs, making it ideal for verifying both correctness and performance improvements.

Here's how you could create a robust synthetic test setup:

Generating Single Frequency Sine Waves

Simple sine waves: Generate single-frequency sine waves where you know exactly what frequency bin should show a peak:

import array
import math

def generate_sine(length, frequency, sample_rate=1.0):
    """Generate a sine wave of specified frequency"""
    data = array.array('f', [0] * length)
    for i in range(length):
        t = i / sample_rate
        data[i] = math.sin(2 * math.pi * frequency * t)
    return data

Generating Multiple Frequencies

Multiple frequency components: Create signals with multiple known frequencies to test frequency resolution:

def generate_composite(length, frequencies, amplitudes, sample_rate=1.0):
    """Generate a signal with multiple frequency components"""
    data = array.array('f', [0] * length)
    for i in range(length):
        t = i / sample_rate
        for freq, amp in zip(frequencies, amplitudes):
            data[i] += amp * math.sin(2 * math.pi * freq * t)
    return data

3. Generate Special Test Cases

Impulse response (single value of 1.0, rest zeros)
Square waves (rich in odd harmonics)
Chirp signals (frequency sweep)
Random noise (to test overall behavior)

4. Create a FFT Test Harness

def test_fft_implementation(fft_function, test_data, expected_peaks=None):
    """Test an FFT implementation against known data"""
    # Copy the data (so original isn't modified)
    data_copy = array.array('f', test_data)

    # Run the FFT
    start_time = time.ticks_us()
    result = fft_function(data_copy)
    elapsed = time.ticks_diff(time.ticks_us(), start_time)

    # Verify peaks if provided
    if expected_peaks:
        for bin_idx, expected_magnitude in expected_peaks:
            actual = math.sqrt(result[bin_idx*2]**2 + result[bin_idx*2+1]**2)
            assert abs(actual - expected_magnitude) < 0.01, f"Expected {expected_magnitude} at bin {bin_idx}, got {actual}"

    return elapsed

5. Benchmark Comparison

def compare_implementations(original_fft, modified_fft, test_cases):
    """Compare performance of two FFT implementations"""
    for name, data, expected in test_cases:
        orig_time = test_fft_implementation(original_fft, data, expected)
        mod_time = test_fft_implementation(modified_fft, data, expected)
        improvement = (orig_time - mod_time) / orig_time * 100
        print(f"{name}: Original: {orig_time}µs, Modified: {mod_time}µs, Improvement: {improvement:.2f}%")

Summary

This approach lets you:

Verify correctness with known frequency components
Measure performance improvements accurately
Test edge cases and special conditions
Ensure that optimizations don't introduce numerical inaccuracies

For the Pico 2 specifically, incorporate different FFT sizes (128, 256, 512, 1024, 2048) to see if your optimizations have different impacts based on data size.