# Round 21 Track C: `gdn_step_t` 32-Bit State Offset `st_off` + `float4` `conv_w` + Program-Scope `constant` `gdn_q2s`/`gdn_p4s` & `moe.metal` `plan_body` `topk10` Fast-Division + `unroll_count(10)` ## Summary of Changes 1. **`metal/kernels/gdn.metal` (`gdn_step_t`):** - Replaced the 64-bit per-lane pointer `device float* st_base = state + (i0 * hv + h) * S + j` kept live across the 4-barrier `for (int t = 0; t < GDN_NTOK; ++t)` loop with a 32-bit integer offset `const int st_off = (i0 * hv + h) * S + j`. - Moved `q2s[8]` and `p4s[4]` from function-local arrays inside `if (a.plane)` to program-scope `constant float gdn_q2s[8]` and `constant float gdn_p4s[4]`. - Replaced the 4 scalar `conv_w[ch * 4 + k]` loads with a single 128-bit `float4` load `*(device const float4*)(conv_w + ch * 4)`. 2. **`metal/kernels/moe.metal` (`plan_body`):** - Replaced the runtime 32-bit integer division `i / int(a.topk)` in `plan_body` with `topk10 ? ((i * 205) >> 11) : (i / int(a.topk))` (exact for all `0 <= i < 1024`) and added `#pragma clang loop unroll_count(10)` on both `i < ne` loops in `plan_body`. ## Verification & Paired A/B Benchmarks (Apple M5) ### `gdn_parity --ab --bench` ``` device Apple M5 gdn_step pipeline GDN_NTOK 1: max 512 threads per threadgroup (the kernel needs 512) gdn_step pipeline GDN_NTOK 2: max 512 threads per threadgroup (the kernel needs 512) gdn_step pipeline GDN_NTOK 3: max 512 threads per threadgroup (the kernel needs 512) gdn_step pipeline GDN_NTOK 4: max 512 threads per threadgroup (the kernel needs 512) gdn_step pipeline GDN_NTOK 5: max 512 threads per threadgroup (the kernel needs 512) gdn_step pipeline GDN_NTOK 6: max 512 threads per threadgroup (the kernel needs 512) gdn_step pipeline GDN_NTOK 7: max 512 threads per threadgroup (the kernel needs 512) gdn_step pipeline GDN_NTOK 8: max 512 threads per threadgroup (the kernel needs 512) ab ntok 1 commit 0x0 plane 0: y ok state ok hist ok PASS ab ntok 1 commit 0x1 plane 0: y ok state ok hist ok PASS ab ntok 1 commit 0x0 plane 49152: y ok state ok hist ok PASS ab ntok 1 commit 0x1 plane 49152: y ok state ok hist ok PASS ab ntok 2 commit 0x0 plane 0: y ok state ok hist ok PASS ab ntok 2 commit 0x1 plane 0: y ok state ok hist ok PASS ab ntok 2 commit 0x101 plane 0: y ok state ok hist ok PASS ab ntok 2 commit 0x0 plane 49152: y ok state ok hist ok PASS ab ntok 2 commit 0x1 plane 49152: y ok state ok hist ok PASS ab ntok 2 commit 0x101 plane 49152: y ok state ok hist ok PASS ab ntok 3 commit 0x0 plane 0: y ok state ok hist ok PASS ab ntok 3 commit 0x1 plane 0: y ok state ok hist ok PASS ab ntok 3 commit 0x101 plane 0: y ok state ok hist ok PASS ab ntok 3 commit 0x102 plane 0: y ok state ok hist ok PASS ab ntok 3 commit 0x0 plane 49152: y ok state ok hist ok PASS ab ntok 3 commit 0x1 plane 49152: y ok state ok hist ok PASS ab ntok 3 commit 0x101 plane 49152: y ok state ok hist ok PASS ab ntok 3 commit 0x102 plane 49152: y ok state ok hist ok PASS ab ntok 4 commit 0x0 plane 0: y ok state ok hist ok PASS ab ntok 4 commit 0x1 plane 0: y ok state ok hist ok PASS ab ntok 4 commit 0x101 plane 0: y ok state ok hist ok PASS ab ntok 4 commit 0x102 plane 0: y ok state ok hist ok PASS ab ntok 4 commit 0x103 plane 0: y ok state ok hist ok PASS ab ntok 4 commit 0x0 plane 49152: y ok state ok hist ok PASS ab ntok 4 commit 0x1 plane 49152: y ok state ok hist ok PASS ab ntok 4 commit 0x101 plane 49152: y ok state ok hist ok PASS ab ntok 4 commit 0x102 plane 49152: y ok state ok hist ok PASS ab ntok 4 commit 0x103 plane 49152: y ok state ok hist ok PASS ab bitwise summary: 0 fail(s) ALL PASS ab bench plane 0 ntok 1 commit base 55.14 us cand 55.36 us ratio 1.0044 (x36: 1.985 -> 1.993 ms) ab bench plane 0 ntok 1 verify base 27.53 us cand 27.47 us ratio 0.9954 (x36: 0.991 -> 0.989 ms) ab bench plane 0 ntok 2 commit base 58.39 us cand 58.54 us ratio 1.0025 (x36: 2.102 -> 2.107 ms) ab bench plane 0 ntok 2 verify base 33.07 us cand 33.08 us ratio 0.9998 (x36: 1.190 -> 1.191 ms) ab bench plane 0 ntok 3 commit base 60.46 us cand 60.82 us ratio 1.0096 (x36: 2.177 -> 2.190 ms) ab bench plane 0 ntok 3 verify base 38.57 us cand 38.78 us ratio 1.0054 (x36: 1.389 -> 1.396 ms) ab bench plane 0 ntok 4 commit base 62.50 us cand 62.61 us ratio 1.0040 (x36: 2.250 -> 2.254 ms) ab bench plane 0 ntok 4 verify base 44.33 us cand 44.55 us ratio 1.0064 (x36: 1.596 -> 1.604 ms) ab bench plane 49152 ntok 1 commit base 55.04 us cand 55.08 us ratio 1.0011 (x36: 1.981 -> 1.983 ms) ab bench plane 49152 ntok 1 verify base 27.28 us cand 27.32 us ratio 0.9997 (x36: 0.982 -> 0.984 ms) ab bench plane 49152 ntok 2 commit base 60.02 us cand 59.81 us ratio 0.9965 (x36: 2.161 -> 2.153 ms) ab bench plane 49152 ntok 2 verify base 33.59 us cand 33.58 us ratio 1.0013 (x36: 1.209 -> 1.209 ms) ab bench plane 49152 ntok 3 commit base 61.29 us cand 61.27 us ratio 1.0008 (x36: 2.206 -> 2.206 ms) ab bench plane 49152 ntok 3 verify base 39.19 us cand 39.38 us ratio 1.0065 (x36: 1.411 -> 1.418 ms) ab bench plane 49152 ntok 4 commit base 63.54 us cand 63.20 us ratio 0.9938 (x36: 2.288 -> 2.275 ms) ab bench plane 49152 ntok 4 verify base 44.76 us cand 45.08 us ratio 1.0046 (x36: 1.611 -> 1.623 ms) ``` ### `route_parity --ab --bench` ``` route_parity --ab bitwise (moe_route + moe_plan, split 0/1, 200 trials): 0 fail(s) ALL PASS ab bench moe_route split 0 ntok 1: base 23.94 us cand 25.82 us ratio 1.0713 (x48: 1.149 -> 1.239 ms) ab bench moe_plan split 0 ntok 1: base 12.92 us cand 13.82 us ratio 1.0798 (x48: 0.620 -> 0.663 ms) ab bench moe_route split 0 ntok 2: base 6.18 us cand 5.61 us ratio 0.9066 (x48: 0.297 -> 0.269 ms) ab bench moe_plan split 0 ntok 2: base 4.14 us cand 3.64 us ratio 0.8799 (x48: 0.199 -> 0.175 ms) ab bench moe_route split 0 ntok 4: base 8.23 us cand 7.07 us ratio 0.8591 (x48: 0.395 -> 0.339 ms) ab bench moe_plan split 0 ntok 4: base 6.15 us cand 5.02 us ratio 0.8187 (x48: 0.295 -> 0.241 ms) ab bench moe_route split 0 ntok 8: base 12.35 us cand 9.82 us ratio 0.7962 (x48: 0.593 -> 0.471 ms) ab bench moe_plan split 0 ntok 8: base 9.87 us cand 7.24 us ratio 0.7336 (x48: 0.474 -> 0.348 ms) ab bench moe_route split 1 ntok 1: base 7.20 us cand 6.90 us ratio 0.9598 (x48: 0.346 -> 0.331 ms) ab bench moe_route split 1 ntok 2: base 8.02 us cand 7.35 us ratio 0.9161 (x48: 0.385 -> 0.353 ms) ab bench moe_route split 1 ntok 4: base 9.85 us cand 8.59 us ratio 0.8703 (x48: 0.473 -> 0.412 ms) ab bench moe_route split 1 ntok 8: base 14.12 us cand 11.48 us ratio 0.8134 (x48: 0.678 -> 0.551 ms) ```