Replace production phase extractor with slope-linear Q512 tables

[falseywinchnet]

Motivation

• Replace machine-dependent tree/vec phase paths with a scalar-friendly, cache-resident slope-linear first-octant extractor (Q=512) specialized for float and double to improve portability and L1 residency.
• Generate all hot-table constants offline at high precision with mpmath and embed them as aligned, constexpr data to avoid runtime trig calls and range-dependent behavior.
• Keep the inverse sin/cos table path intact and NaN-safe while ensuring forward mag/phase conversion is dense and sequential over standard bin order.
• Add correctness and benchmark infrastructure to validate accuracy and performance of the new slope-linear paths.

Description

• Added a small generic table type and specializations in src/detail/generated/bruun_phase_slope_tables.hpp for bruun_phase_slope_tables<float,128,512> and bruun_phase_slope_tables<double,256,512> with alignas(64) constants and a std::uint8_t slope_to_leaf[513] map.
• Implemented bruun_phase_slope_leaf and a generic bruun_phase_first_octant_slope_linear<T,Leaves,Q> function plus type-specific wrappers bruun_phase_first_octant and bruun_phase_first_octant_f32 and float overloads of bruun_fused_madd/bruun_fused_msub in src/detail/bruun_kernel.hpp.
• Replaced tree/vec production first-octant and pair/SIMD wrappers on the hot path so bruun_phase_atan2_mag / bruun_phase_atan2_mag_f32 now use the slope-linear tables and quadrant repair; the forward mag/phase conversion loop was kept sequential over standard-order bins in convert_standard_complex_to_mag_phase.
• Added tools/gen_phase_slope_tables.py (mpmath, 100 dps) to regenerate tables, updated examples/atan2_benchmark.cpp labels to the new slope paths, added examples/audio_magphase_roundtrip_benchmark.cpp, and added a dense slope accuracy test check_slope_phase_accuracy in tests/correctness.cpp plus a relaxed mag/phase tolerance in tests/api_c.c to match the double target.

Testing

• Built the project with cmake -S . -B build && cmake --build build -j and the build completed successfully.
• Ran unit/regression tests with ctest --test-dir build --output-on-failure and all tests passed (reported 2 tests in the CI run: correctness and api_c).
• Executed the phase benchmark ./build/atan_vectoring_network_experiment 4194304 which produced: bfft slope256 linear double: 0.260033 s, 16.130 Mphase/s, bfft slope128 linear float: 0.283724 s, 14.783 Mphase/s, and bfft table sincos: 0.146617 s, 28.607 Mpair/s.
• Executed the audio round-trip benchmark ./build/audio_magphase_roundtrip_benchmark 2048 4096 which produced split timings and accuracy metrics including magphase fwd+inv 0.594445 s, MSE 1.2865420194109656e-20, SNR 193.138900 dB, and max_abs 2.043787084016202e-10.

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Codex Task