# Round 27 Track C Audit Report: `gdn_step_t` (`gdn.metal`) Barrier Elimination (`5 -> 4` Barriers/Token) + `dt`/`ssm_a` Hoist + `part[8]`/`red2[IB-1]` Shrink - **Agent**: `argon-r27-gdn-and-gr-opt` (`gemini-4-argon`) - **Patch**: `/tmp/argon_r27_gdn/argon_r27_gdn.patch` (`git -C vendor/strata apply --check /tmp/argon_r27_gdn/argon_r27_gdn.patch` passes cleanly) - **Owned files**: `metal/kernels/gdn.metal`, `metal/tests/gdn_parity.cpp` (`vendor/strata/` untouched) ## 1. Summary of Changes 1. **Barrier Elimination (`5 -> 4` `threadgroup_barrier`s per Token) + `part[32] -> part[8]` Shrink (`metal/kernels/gdn.metal`)**: - Before the first barrier of each token, threads `0..127` (`sg = 0..3`) and `128..255` (`sg = 4..7`) already hold raw `cv` in registers: they now write raw `qs[tid] = cv` and `ks[tid - 128] = cv` directly to shared memory alongside their `simd_sum(cv * cv)` write to `part[sg]`, while threads `256..383` (`sg = 8..11`) write `vs[tid - 256] = cv` (skipping redundant `simd_sum(cv * cv)` on `tid >= 256` and shrinking `threadgroup float part[32]` to `part[8]`) and idle lanes `384` / `416` compute `gb[0]` / `gb[1]`. - After that single barrier, each thread computes `rsq = rsqrt(tot_q / float(S) + a.eps / float(S))` and `rsk = rsqrt(tot_k / float(S) + a.eps / float(S))` from `part[0..7]` and normalizes `kl = (rsk * ks[qk_idx]) * scale` and `ql = (rsq * qs[qk_idx]) * scale` on the fly before broadcasting across the simdgroup. - Because `(rsk * ks[qk_idx]) * scale` and `(rsq * qs[qk_idx]) * scale` execute the exact same two IEEE-754 roundings `(rs * cv) * scale` in the exact same order on the exact same `cv` value, the result is 100% bitwise identical while eliminating `GDN_NTOK` 512-thread barriers per dispatch (`144` barriers per 4-token verify window across 36 GDN layers). - Write-after-read safety across tokens `t -> t + 1` holds with three subsequent barriers in token `t` separating all reads of `qs`, `ks`, `vs`, `part`, and `gb` from their next-token writes. 2. **Token-Invariant `dt[h]` & `ssm_a[h]` Hoist + `red2[IB][S] -> red2[IB - 1][S]` Shrink (`metal/kernels/gdn.metal`)**: - Preloaded `dth = tid == 384 ? dt[h] : 0.0f` and `ssm_ah = tid == 384 ? ssm_a[h] : 0.0f` before the `state` load loop and token loop so their device loads issue in parallel with `qkv`, `hist`, `conv_w`, `gamma`, and `state`. - Shrunk `threadgroup float red2[IB][S]` to `red2[IB - 1][S]` (saving `512 B` of threadgroup memory; total threadgroup memory drops `5784 B -> 5176 B` for `IB = 4`): `ib == 0` keeps its partial readout `o` in its register across the barrier and accumulates `for (int k = 0; k < IB - 1; ++k) o += red2[k][j]`, preserving the exact IEEE-754 addition order `((o_0 + o_1) + o_2) + o_3` while eliminating 128 shared stores and 128 shared loads + additions per token. - Tested `#pragma clang loop unroll(full)` on `for (int t = 0; t < GDN_NTOK; ++t)` and ruled it out: full unrolling of the outer token loop degraded `ntok >= 4` performance by `+6% .. +16%` due to register pressure under `[[max_total_threads_per_threadgroup(512)]]`. 3. **Extended `gdn_parity --ab` Coverage to `ntok = 1..8` (`metal/tests/gdn_parity.cpp`)**: - Updated `--ab` bitwise parity and paired A/B benchmark loops in `metal/tests/gdn_parity.cpp` from `ntok = 1..4` to `1..MAXT` (`1..8`), covering all 88 `(ntok, commit, plane)` combinations (`commit = 0`, `1`, `0x101 .. 0x107`; `plane = 0`, `49152`) in `< 4.2s` total runtime. ## 2. Verification & Paired A/B Benchmark Results on Apple M5 - **Pipeline threadgroup occupancy**: - `gdn_step` (`IB = 4`): `maxTotalThreadsPerThreadgroup = 512` (needs `512`) for all `GDN_NTOK = 1..8`. - `gdn_step8` (`IB = 8`): `maxTotalThreadsPerThreadgroup = 1024` (needs `1024`) for all `GDN_NTOK = 1..8`. - **Bitwise parity (`gdn_parity --ab /tmp/argon_r27_gdn/base_gdn.metal`)**: - `gdn_step` (`IB = 4`): **88 / 88 PASS** (`0 fail(s) ALL PASS`, `memcmp == 0` on `y`, `state`, `hist` across all `ntok = 1..8`, `commit = 0/1/partial`, `plane = 0/49152`). - `gdn_step8` (`IB = 8`): **88 / 88 PASS** (`0 fail(s) ALL PASS`). - **Paired A/B Benchmark (`./build-metal/gdn_parity --ab /tmp/argon_r27_gdn/base_gdn.metal --bench`, 36 layers rotated = 113 MB state)**: ```text ab bench plane 0 ntok 1 commit base 59.03 us cand 58.54 us ratio 0.9885 (x36: 2.125 -> 2.107 ms) ab bench plane 0 ntok 1 verify base 35.23 us cand 34.51 us ratio 1.0120 (x36: 1.268 -> 1.242 ms) ab bench plane 0 ntok 2 commit base 67.51 us cand 66.34 us ratio 0.9924 (x36: 2.430 -> 2.388 ms) ab bench plane 0 ntok 2 verify base 41.03 us cand 40.69 us ratio 0.9915 (x36: 1.477 -> 1.465 ms) ab bench plane 0 ntok 3 commit base 67.96 us cand 73.18 us ratio 1.0698 (x36: 2.447 -> 2.635 ms) ab bench plane 0 ntok 3 verify base 53.70 us cand 49.92 us ratio 0.9458 (x36: 1.933 -> 1.797 ms) ab bench plane 0 ntok 4 commit base 85.32 us cand 82.23 us ratio 0.9813 (x36: 3.071 -> 2.960 ms) ab bench plane 0 ntok 4 verify base 66.33 us cand 61.44 us ratio 0.9449 (x36: 2.388 -> 2.212 ms) ab bench plane 0 ntok 5 commit base 97.72 us cand 97.38 us ratio 0.9693 (x36: 3.518 -> 3.506 ms) ab bench plane 0 ntok 5 verify base 76.71 us cand 71.98 us ratio 0.9729 (x36: 2.762 -> 2.591 ms) ab bench plane 0 ntok 6 commit base 105.55 us cand 107.56 us ratio 1.0220 (x36: 3.800 -> 3.872 ms) ab bench plane 0 ntok 6 verify base 85.64 us cand 80.99 us ratio 0.9284 (x36: 3.083 -> 2.916 ms) ab bench plane 0 ntok 7 commit base 115.73 us cand 109.36 us ratio 0.9450 (x36: 4.166 -> 3.937 ms) ab bench plane 0 ntok 7 verify base 92.26 us cand 83.80 us ratio 0.9412 (x36: 3.321 -> 3.017 ms) ab bench plane 0 ntok 8 commit base 121.96 us cand 113.98 us ratio 0.9386 (x36: 4.390 -> 4.103 ms) ab bench plane 0 ntok 8 verify base 98.90 us cand 93.92 us ratio 0.9496 (x36: 3.561 -> 3.381 ms) ab bench plane 49152 ntok 1 commit base 61.16 us cand 60.90 us ratio 0.9698 (x36: 2.202 -> 2.193 ms) ab bench plane 49152 ntok 1 verify base 39.40 us cand 38.15 us ratio 0.9683 (x36: 1.418 -> 1.373 ms) ab bench plane 49152 ntok 2 commit base 69.72 us cand 67.33 us ratio 0.9847 (x36: 2.510 -> 2.424 ms) ab bench plane 49152 ntok 2 verify base 47.07 us cand 46.84 us ratio 0.9995 (x36: 1.695 -> 1.686 ms) ab bench plane 49152 ntok 3 commit base 77.60 us cand 75.86 us ratio 0.9621 (x36: 2.794 -> 2.731 ms) ab bench plane 49152 ntok 3 verify base 57.29 us cand 56.05 us ratio 0.9837 (x36: 2.062 -> 2.018 ms) ab bench plane 49152 ntok 4 commit base 94.69 us cand 86.28 us ratio 0.9218 (x36: 3.409 -> 3.106 ms) ab bench plane 49152 ntok 4 verify base 67.10 us cand 64.39 us ratio 0.9207 (x36: 2.415 -> 2.318 ms) ab bench plane 49152 ntok 5 commit base 106.59 us cand 101.82 us ratio 0.9709 (x36: 3.837 -> 3.666 ms) ab bench plane 49152 ntok 5 verify base 79.16 us cand 75.86 us ratio 0.9398 (x36: 2.850 -> 2.731 ms) ab bench plane 49152 ntok 6 commit base 115.77 us cand 109.96 us ratio 0.9570 (x36: 4.168 -> 3.959 ms) ab bench plane 49152 ntok 6 verify base 95.05 us cand 88.38 us ratio 0.9473 (x36: 3.422 -> 3.182 ms) ab bench plane 49152 ntok 7 commit base 126.66 us cand 118.77 us ratio 0.9567 (x36: 4.560 -> 4.276 ms) ab bench plane 49152 ntok 7 verify base 102.09 us cand 96.49 us ratio 0.9493 (x36: 3.675 -> 3.474 ms) ab bench plane 49152 ntok 8 commit base 127.43 us cand 120.34 us ratio 0.9517 (x36: 4.587 -> 4.332 ms) ab bench plane 49152 ntok 8 verify base 109.12 us cand 102.96 us ratio 0.9830 (x36: 3.928 -> 3.707 ms) ```