perf: optimize every custom periodogram implementation across all backends

[tjayasinghe]

Implements the full optimization plan across all custom (non-reference) periodogram implementations — numpy, numba, cupy RawKernel, and torch/array-API tiers — plus the extension of the multicore numba CPU tier from BLS to all six ported methods.

Algorithmic (all backends at once)

• MHAOV: Gram matrix assembled from harmonic trig sums (Chebyshev recurrence, one cos/sin evaluation) instead of the (F,N,2H+1) design tensor — ~3x on numpy/cupy/torch, an order of magnitude less transient memory, gemm-free by construction (Blackwell cuBLAS workaround deleted).
• GLS direct path: one trig evaluation instead of six (shared base-grid angles + double-angle identities) — ~1.8x on torch CPU/CUDA; frequency chunk auto-capped by N.
• PDM: fold binned once into n_bins*n_covers fine bins; covers regrouped exactly — ~2.8x numpy, 3x fewer CUDA atomics.

New numba CPU tier (PDM, CE, String-Length, MHAOV, TLS)

prange kernels mirroring the CUDA designs; cpu/auto resolve to them via a shared fast_cpu_backend attribute (replaces the bespoke BLS override). Warm speedups vs the vectorized numpy paths: PDM 306x, CE 135x, MHAOV 57x, TLS 53x, SL 23x; parity <= 2.5e-11 (TLS bit-identical; SL stable-sort tie order preserved via mergesort).

GPU

• float32-templated RawKernels (BLS/PDM/CE/TLS) honoring precision: ~8.6x for BLS (610->71 ms segmented) and TLS on GeForce-class FP64-limited cards; float64 remains the default; float32 BLS guards empty windows with a sum-scaled ivar floor.
• String-Length CUDA kernel: stable in-block bitonic sort — 75x over numpy, ~2x the old vectorized cupy path; torch path fuses sort+gather via torch.sort(stable=True).
• CE: exact int shared-memory count atomics (half the smem) + block-parallel entropy reduction.
• BLS device cache: one upload per light curve across period segments (cupy+torch), host-side t_min (no per-segment sync), one stacked D2H for the 7 outputs.
• GLS NUFFT: base-grid pair batched as one n_trans=2 transform (finufft + cufinufft plan cache); one-shot cufinufft assembles on device (194->290 lc/s).

Shims

scatter_add numpy via buffered bincount (vs unbuffered add.at), cupy via cupyx.scatter_add; new row-wise scatter helpers avoid materializing (P,N) broadcast copies on torch. ensure_shared_memory now opts in on dynamic+static totals (fixes a CUDA_ERROR_INVALID_VALUE edge at exactly 48 KB).

Not included (documented reasoning)

• TLS Ofir grid: requires physical stellar-density durations, which breaks TLS's period-independent phase-bin widths — a scientific redesign, not an optimization.
• TLS FFT correlation: break-even at n_bins=256 and rounding can flip the dip-admissibility test.

Verification

233 tests pass (12 new in tests/test_fast_backends.py, incl. GPU float32 and tie-stability checks) on a machine with numba + cupy + CUDA torch (Blackwell); ruff and mypy --strict clean; docs build with -W. All measured speedups are in the commit messages; checksums/parities quoted per commit.

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