Add FFTW rectangular/polar round-trip benchmark with dynamic loading and SFDR metrics

[falseywinchnet]

Motivation

• Provide a focused example that compares BFFT and FFTW round-trip quality and throughput in both rectangular and polar domains for double and float precisions.
• Use FFTW’s planner with selectable modes (default MEASURE) while keeping the build independent of FFTW headers or link-time libraries by using dynamic dlopen/dlsym resolution.
• Add meaningful polar-quality diagnostics (magnitude-dB, phase-radians) and simple SFDR spur metrics to evaluate polar reconstructions.

Description

• New example examples/fftw_polar_roundtrip_benchmark.cpp implementing deterministic multi-frame input generation, BFFT and FFTW double/float paths, polar conversion using atan2/sin/cos, and separate timing for forward/inverse/combined loops.
• Dynamic FFTW/FFTWf loading via dlopen/dlsym, resolving fftw_plan_dft_r2c_1d, fftw_plan_dft_c2r_1d, fftw_execute, fftw_destroy_plan, fftw_malloc, fftw_free and their float (fftwf_) variants, plus optional metadata fftw_version, fftw_cc, fftw_codelet_optim (prints n/a when missing and reports NEON presence via string search).
• Local FFTW flag constants defined (FFTW_MEASURE_FLAG, FFTW_ESTIMATE_FLAG, FFTW_PATIENT_FLAG, etc.) with CLI options --fftw-measure (default), --fftw-estimate, and --fftw-patient, and CLI flags --sfdr/--no-sfdr and --help.
• Polar quality and SFDR: compute magnitude-dB and wrapped phase error with bin masking, implement O(M^2) DFT-based spur search (skips heavy work for very large M), and report complex rebuild max/RMS dBc along with mag/phase spur metrics.
• CMake: added example target fftw_polar_roundtrip_benchmark and configured it to output into build/examples and link dl when available so the project builds without FFTW present.

Testing

• Built the project: cmake -S . -B build and cmake --build build -j completed successfully.
• Ran the test suite: ctest --test-dir build --output-on-failure and all tests passed.
• Executed the example binary with representative arguments and flags: ./build/examples/fftw_polar_roundtrip_benchmark 64 4 --no-sfdr and ./build/examples/fftw_polar_roundtrip_benchmark 64 4 --sfdr, both ran and produced the expected benchmark and SFDR output (FFTW rows are gracefully skipped when libraries are not found).

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Codex Task