# ReLU Optimization for RTX 4090 (sm_89)

> **Erratum (2026-07-31, see `L2_BAND_CLIFF.md`):** this doc records the
> original v1 tuning. Two of its conclusions were later corrected: the
> vs-torch/vs-Hub margins measured with shared-buffer interleaves were
> position-biased (v3 numbers: ~parity vs torch for fp32 on the 4090),
> and the "streaming everywhere ≥ 32 MB" config had a real 0.34–0.65x
> cliff vs torch for working sets in (32 MiB, L2] — the sweep below never
> sampled that band (its sizes jump 33.6 MB → 134 MB). Fixed in v3 with
> default loads + streaming stores in-band. The sweep's DRAM-wall
> findings and config rankings *within* the same measurement layout
> remain valid.

Float32 ReLU (`out[i] = max(in[i], 0)`) tuned for the NVIDIA RTX 4090 (Ada,
sm_89), built via kernel-builder (torch212-cu126) and benchmarked with the
official `kernels` ReluBenchmark plus controlled timing. Method: empirical
design-space sweep + independent design fan-out + roofline analysis.

## TL;DR

Deployed kernel (`relu_cuda/relu.cu`): **float4 vectorized + streaming
load/store (`__ldcs`/`__stcs`) + adaptive block size (128 L2-resident / 512
DRAM), unroll 1, flat grid-stride, scalar tail.**

| Workload | Hub (orig) | Optimized | torch.relu | Optimized result |
|----------|:---:|:---:|:---:|:---|
| base 1024² (L2) | 1836 GB/s | **2335 GB/s** | 2285 | **1.27× vs Hub, beats torch** |
| large 4096² (DRAM) | 940 GB/s | **945 GB/s** | 936 | at the roofline (1.01×) |

Bit-identical to the upstream kernel on all inputs (incl. NaN→0). Correctness
verified incl. tail sizes 4097/333/1.

## Method (ultracode)

1. **Empirical sweep** (`bench/sweep.cu`, nvcc -arch=sm_89 -O3): 31 configs
   × 8 sizes (64K → 134M elems), each correctness-checked, CUDA-event timed.
   Configs = {vec2,vec4,scalar} × unroll{1,2,4} × store{default,`__stcs`} ×
   load{default,`__ldcs`} × block{128,256,512}.
2. **Design fan-out** (5 independent senior-engineer agents + roofline analyst).
   The streaming agent verified in SASS that `__ldcs/__stcs` lower to
   `LDG.E.EF.128 / STG.E.EF.128` (Evict-First, not a hard L2 bypass on sm_89) —
   explaining why the large-case gain is small.
3. **Roofline**: theoretical 1008 GB/s; practical achievable copy ~960; ReLU
   target ~955. So 942→ceiling headroom is only ~+1.5–2% (in the noise).

## What the sweep proved

- **DRAM-bound large (working set > ~50 MB): hard wall ~944 GB/s (93.7% of
  peak, ~98% of the ~960 practical achievable).** Every config — scalar to
  float4, streaming or not, any block/unroll — lands 940–945. Nothing beats the
  wall.
- **unroll ≥ 4 is consistently SLOWER on large** (929–936) — register pressure.
  This is why the earlier "v2" (ILP-4 + occupancy-capped grid) regressed.
- **Under-subscribing the grid (v2's other bug) costs ~2%** — keep a full grid.
- **L2-resident (≤ ~33 MB): streaming load+store wins.** On base 1024²,
  `float4 + __ldcs + __stcs + block128` = 2357 GB/s in the microbench (2335 in
  the kernels harness) vs 2218 for plain float4 — **+6%, and ahead of torch**.
  Streaming avoids L2 write-allocate pollution; smaller blocks balance SMs.
- **Block size only matters in the L2 regime**: 128 best for ≤~2–4 M elems,
  512 for the 16–33 MB band; irrelevant on DRAM. Hence the adaptive threshold.

## Why not "more"?

The large case is memory-bound at the GDDR6X wall — a read+write elementwise op
cannot exceed copy bandwidth. ILP, wider vectors, bigger grids, streaming: all
measured flat-or-worse on large. The only real headroom is L2-resident sizes,
which the streaming + block-128 path captures. Knowing when to stop is the
optimization.

## Semantics

`out = x > 0 ? x : 0` (matches upstream kernels-community/relu exactly,
including NaN→0). PyTorch's `F.relu` propagates NaN→NaN; the upstream kernel and
this one return 0 for NaN. This is a pre-existing upstream semantic, intentionally
preserved — the optimization is performance-only, not a numerics change.

## Reproduce

```
# microbench sweep
cd bench && nvcc -arch=sm_89 -O3 -o sweep sweep.cu && ./sweep
# build + official benchmark
cd relu-build && kernel-builder build --variant torch212-cxx11-cu126-x86_64-linux
kernels benchmark kernels-community/relu --version 1     # official Hub baseline
```