Experimental warp-shared LU and Cholesky

中文 implementation/verification guide

Explicit new APIs in rusolver::tensor behind the OFF-by-default warp-solvers feature (cuda,warp-solvers for NVIDIA; the runner enables both):

• cholesky_solve_batched_warp(a, b, BatchedCholeskyOptions)
• lu_solve_batched_warp(a, b, BatchedLuOptions)

One full 32-thread block owns each small FP32 system. Striped/coalesced global loads feed shared matrix/RHS scratch; independent rows and RHS columns are assigned to lanes. LU uses warp max/min pivot selection, preserving the first maximum tie rule. Odd shared pitch avoids duplicate banks for fixed-column 32-bit row accesses in a 32-bank model. All memory handoffs use block barriers; no implicit warp lockstep or lane-local exits around synchronization.

n=1..32, nrhs=1..8, contiguous row-major, same device/queue. Requires fixed 32-lane plane operations and sufficient block/shared/grid limits. Inputs are unchanged, outputs are new allocations, numeric failure zeros the entire failed system and returns the existing status codes. No CPU fallback, casting or hidden diagonal jitter. The existing serial APIs remain the default.

At n=32/nrhs=8, shared declarations consume 5248 bytes/block for Cholesky and 5376 for LU. Intermediate global scratch accesses are replaced with shared accesses. These are source-level facts, NOT DRAM counters or measured speedup. One warp/block can reduce occupancy at a resident-block limit; tiny systems may be slower. No automatic crossover policy is installed.

python tools/run_kernel_optimization_regressions.py --suite plan
python tools/run_kernel_optimization_regressions.py --suite build
python tools/run_kernel_optimization_regressions.py --suite cuda --compiler both
python tools/run_kernel_optimization_regressions.py --suite sanitizer --compiler both
python tools/run_kernel_optimization_regressions.py --suite bench --compiler both --batch 256 --order 16 --rhs 4

plan compiles the real standalone Rust launch planner; build expands device macros via Cargo; CUDA tests include the original baseline tests. Sanitizer runs memcheck/racecheck/synccheck with nonzero error exits. The benchmark warms both paths, alternates measurement order, checks every output vs FP64 solve and factor/residual references, and reports synchronized API wall time INCLUDING allocation/submission/completion. No GPU-only event timing is claimed.