Thread-scoped operations (glass::thread::)#

Sequential, one-problem-per-thread variants of the branch-free primitives: a single thread owns the whole operation — no barriers, no shuffles, no threadIdx read — so 32 independent problems pack into one warp. They target the low-DOF corner (robot DOF ≲ 7) where even a warp per problem leaves most lanes idle: a thread-per-problem launch (<<<ceil(P/TPB), TPB>>>, see glass::suggested_threads_per_block<>()) keeps every lane busy on its own problem.

Contract: compile-time sizes only. The tier’s value is operands that nvcc keeps register-resident, which requires fully-unrolled, compile-time-resolvable indexing — the measured ceiling is N ≤ 7 (both dtypes; larger N still computes correctly but demotes the operands to local memory, forfeiting the tier’s premise). Operands may be thread-local register arrays; nothing is read from threadIdx, so the functions are launch-shape-agnostic.

Every op delegates to the same *_impl body its block-scoped sibling uses, collapsed through ThreadBarrier (rank 0, size 1, no-op sync) — the same algorithm and operand order as glass::block:: on one thread, agreeing to within a few ULP (FMA contraction may differ between the two instantiations; test/test_thread.py pins the bound). They live in the same base headers as their block-scoped siblings (under namespace thread), so their rendered signatures appear on the L1 — Vector Operations, L2 — Matrix-Vector Operations, and L3 — Matrix Operations pages.

Deliberately absent (see the glass::thread:: constraints block in CLAUDE.md): the _fast / _lowmem reduction twins (they name reduction strategies; one thread has none — thread::dot simply returns a serially accumulated T), the contraction-parallel *_reduced family, and every data-dependent / pivoted op (iamax, pivoted ldlt, getrf / gesv, inv_pivoted, syev) — when every lane owns a different problem, a data-dependent branch diverges the whole warp, which is exactly the cost the tier exists to avoid.

Surface (mirrors the branch-free warp surface):

  • L1: dot (returns T), the serial reductions reduce / nrm2 / asum / nrm1_diff, and the maps axpy / axpy_strided / scal / copy / copy_strided / rot / symmetrize. See L1 — Vector Operations.

  • L2: gemv (flags: TRANSPOSE / ROW_MAJOR), trsv (FillMode / Diag / TRANSPOSE). See L2 — Matrix-Vector Operations.

  • L3: gemm, syrk / syr2k, trsm, the factor/solve chain potrf / posv / potrs / ldlt (non-pivoted) / ldlt_solve / inv (non-pivoted), and the fused families tensor_vec_contract / vec_tensor_vec, congruence_sym / bilinear / congruence_accum, riccati_gain. See L3 — Matrix Operations.

The dispatch ladder (Backend Picker (glass-defaults.cuh)) contends the tier alongside warp / block / nvidia, and the sm_120 tables ship thread verdicts (2026-07-18 sweep): thread takes the low-DOF corner of every op except gemm — up to 7.5× on posv f64 at N≤6 (docs sweep-results page + bench/RESULTS.md). Run bench/tune.py --sm auto to contend it on your own GPU.