Table-based sin/cos approximation and residue-linear traversal + unrolling for mag/phase paths

[falseywinchnet]

Motivation

• Reduce expensive sin/cos calls in inverse mag/phase hot loops and improve cache locality and throughput for forward/inverse mag-phase transforms.
• Provide a fast fallback that preserves correct behavior for out-of-range phase inputs while enabling a fast path for phases in [0, 2*pi).
• Improve performance by traversing Bruun residues in linear/native order and applying small-loop unrolling in the inverse hot path.

Description

• Added #include <array> and new types bruun_sincos_sample and templated bruun_sincos_table<K> to precompute a power-of-two sin/cos lookup table.
• Implemented bruun_table256_poly3_sincos and bruun_table256_poly3_sincos_f32 which perform a table lookup plus a cubic polynomial correction for remainder, and fall back to std::sin/std::cos for out-of-range phases.
• Rewrote forward mag/phase paths to traverse residues in native linear order using IDX (improving streaming reads) and removed redundant phase-normalization code now handled by bruun_phase_atan2_mag.
• Replaced direct std::sin/std::cos calls in inverse_mag_phase and inverse_mag_phase_f32 with the table-based approximations, and added 4-element loop unrolling to compute sin/cos for multiple bins per iteration.

Testing

• Built the library and ran the full unit test suite; all unit tests completed successfully.
• Ran the mag/phase correctness tests comparing round-trip forward/inverse; results matched baseline behavior.
• Executed performance microbenchmarks for mag/phase inverse and forward hot paths; observed expected throughput improvements (benchmark runs succeeded).

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Codex Task