perf: rasterizer and pipeline optimizations

[rayanht]

garden, 1535033 gaussians, 1297x840, SH degree 3, densification off.

BENCHMARK=1 PROFILE_STAGES=1 msplat garden --resume garden_nd0.ply -n 500 \
  --num-downscales 0 --warmup-length 999999 --sh-degree-interval 1

9s/run, +/-0.2%.

Landed

#	change	rast_fwd	rast_bwd	sum
0	v1.1.4 (6b81971)	1.674	4.453	12.50
1	threadgroup read instead of simd_broadcast	1.674	3.750	11.76
2	per-subtile candidate compaction	1.202	3.223	10.78
3	Morton-order gaussians at each densification	1.198	3.203	10.22

(3) is measured on an offline-reordered PLY to isolate it: proj_sh_fwd 0.853 -> 0.654,
sort 1.366 -> 1.206, grad_stats 0.120 -> 0.064, adam 2.884 -> 2.787. The rasterizers
do not move; they read packed_* in sorted order and were already coherent.

Full runs, v1.1.4 -> head of branch:

config	before	after	PSNR	SSIM
--num-downscales 0	82s	67.7s	25.72 -> 25.68	0.7838 -> 0.7835
--num-downscales 2	32.4s	29.4s	24.91 -> 24.93	0.7151 -> 0.7153

nd0 PSNR spread across runs is 0.12, nd2 0.05.

Breakdown

stage	ms	%
rast_bwd	3.223	29.9
proj_sh_bwd_adam	2.901	26.9
sort/scatter/pack	1.366	12.7
rast_fwd	1.203	11.2
loss_fwd_bwd	1.112	10.3
proj_sh_fwd	0.849	7.9
grad_stats	0.120	1.1
sum	10.776
ms/iter	11.42
unattributed	0.64

rast_bwd ablations (post-compaction, 3.199ms)

variant	rast_bwd	removed part
base	3.199
no atomics	2.910	atomics 0.289 (9.0%)
no simd reductions	2.507	reductions 0.692 (21.6%)
loop floor	1.105	per-lane work 2.094 (65.5%)

floor 1.105 (34.5%) / gradient math 1.113 (34.8%) / reductions 0.692 (21.6%) / atomics 0.289 (9.0%).
Compaction cut the floor 2.83 -> 1.105; atomics and reductions unchanged in absolute terms.

sort/scatter/pack ablations (1.376ms)

part	ms
scatter_to_prealloc_bins + prefix_sum + bin load	1.139
pack (gather by gaussian id)	0.170
bitonic sort	0.067

1.88M atomic_fetch_add onto 4346 tile counters. Contention ruled out (see below);
the 1.139ms is bbox iteration plus 1.88M x 8B writes into prealloc_bins.

Queue

• loss_fwd_bwd 1.11ms: loss_intermediates + ssim_h_buf are [H,W,15], ~65MB each, ~260MB round-trip vs ~0.65ms roofline.
• compaction in the chunked kernels (4x-downscale phase only).
• fold grad_stats into proj_sh_bwd_adam, ~0.1ms.

Ruled out

change	result
transpose SH for coalescing	proj_sh_bwd_adam 2.885 -> 4.67
16x16 rasterization threadgroups	sum 11.815 -> 12.209
ballot-skip the 9 simd_sum when 1 lane is valid	rast_bwd 3.228 -> 3.144, sum flat. Single-lane is only ~12% of cases.
radix instead of bitonic	bitonic is 0.067ms of the 1.376ms stage. Nothing to win.
warp-aggregated scatter atomics	spreading counters to remove contention: stage 1.364 -> 1.558. Contention is not the cost; tile-local counters cache well. Re-tested under Morton order (higher contention): 1.211 -> 1.342. Same answer.
deferred ("lazy") Adam for means/scales/quats/opacities	dense geometry Adam costs 0.913ms (adam 2.832 -> 1.919 when ablated). Replaying the missed zero-gradient steps in registers is exact, and gave -6.2% wall. But the catch-up lands in the backward, after the forward already projected with stale parameters: SSIM 0.7820-0.7824 vs a 0.78355-0.78457 baseline band over 10 runs. Bounding staleness with a flush every 10 steps recovers SSIM to 0.78329 but halves the win to -3.4%. Correct fix is to catch up inside project_and_sh_forward, which costs back most of the saving.

proj_sh_bwd_adam is bandwidth bound: 507K visible x 1284B = 651MB/iter.

Notes

• Full 7000-iteration runs: +/-4s spread, cannot resolve <2s. Quality checks only.
• metal_tensor.hpp changes sizeof(MTensor). Incremental builds across it produce a mixed-ODR binary that trains to garbage. rm -rf build after any header change.