woutermans
0fe3a28cb7
Per-layer staged-image engine for the eleven translated denoiser Swin layers: descriptors (verified offsets per phase), cut recipes that splice an isolated native phase into NVIDIA's PTX, wave templates, epilogue notes and GPU probes. The isolated phase-8 splice produces a byte-identical final 4K frame but is slower than the translated body (14.90 vs 6.59 ms) - a correctness experiment, not a shipping improvement; docs/rr-engine.md records the design and the next direct-converter win (B operands built from transposed accumulators).
800 lines
47 KiB
Markdown
800 lines
47 KiB
Markdown
# `cuda_dldn_engine_swin_enc4_kernel` — the epilogues of phases 1…62
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Companion to `kernels/rr/rr_layer_spec.py enc4`. Everything below was read out of
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`~/.cache/d4r-rr-corpus/0017-PREPASS_ENTRYPOINT_NAME.ptx`, entry
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`cuda_dldn_engine_swin_enc4_kernel`.
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## 0. Conventions
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* **`sNNNN` is a statement index** in the linearisation `rr_layer_spec.py`
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documents (statements of the entry body; a wrapped `{ … }` block and a 4-line
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`mma.sync` count as one statement, numbered at its first line). **`LNNNNN` is
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the physical line** of the same instruction in the corpus file, so every claim
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can be checked with `sed -n 'LNNNNN,LNNNNN p' …ptx`.
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* An **epilogue** is the run of statements between one phase's last `mma` and the
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next phase's first `mma`.
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* `W` denotes the prepared weight image: `ld.param.u64 %rd2,
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[cuda_dldn_engine_swin_enc4_kernel_param_0+40]` (s9), globalised as
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`cvta.to.global.u64 %rd3, %rd2` (s10). Every `ld.weak.global.ca.v4.u32` in an
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epilogue reads `W + 16*laneid + imm`. (s20229 re-reads the same parameter; the
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pointer is not cached.)
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* `S` denotes the plane arena: `param_0+48`, reached as
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`ld.param.u64 %rd808, [%rd1+-32]` with `%rd1 = param_0+80` (`add.s64 %rd1,
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%rd9, 80`, s4) then `cvta.to.global.u64 %rd5, %rd808` (s19817–s19818).
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* The C/D register layout and the weight-addressing formula are fixed (see the
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settled notes): `C/D reg0 = (row g, cols 2t,2t+1)`, `reg1 = (row g+8, same cols)`,
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`g = laneid>>2`, `t = laneid&3`.
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* `rr_layer_spec.py`'s printed `M`/`N`/`K` come from `geom()` (distinct A/B
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fragment counts and accumulator-chain length). The `Phase` object's own
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`w_min..w_max`/`n_tiles`/`k_slots` fields use a different (512-byte-block)
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convention and disagree with `geom()` on the stem phases; §2 uses `geom()` and
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checks the arithmetic explicitly.
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* Anything I could not pin down from the PTX is in §6 under **uncharacterised**.
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## 1. Shared vocabulary
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### 1.1 Addresses and parameters an epilogue touches
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| symbol | how it is obtained | statements |
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|---|---|---|
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| `W` (weight image, 533844 bytes) | `ld.param.u64 %rd2, [param_0+40]` | s9 (re-read s20229, s21313) |
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| `S` (plane arena, `param+48`) | `ld.param.u64 %rd808, [%rd1+-32]` → `cvta.to.global.u64 %rd5, %rd808` | s19817–s19818 |
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| output buffer (`param+56`) | `ld.param.u64 %rd849, [%rd945+-24]` with `%rd945 = param_0+80` | s21037–s21038 |
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| input plane (`param+8`) | `ld.param.u64 %rd11, [%rd1+-72]` → `cvta.to.global.u64 %rd4, %rd11` | s22–s23 |
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| extents `(ex, ey)` | `ld.param.v2.u32 {%r575, %r576}, [param_0+0]`; re-read as `ld.param.v2.u32 {%r29719, %r29720}, [%rd940+-80]` | s15; s20222 |
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| block origin `(x0, y0)` | `%r570 = ctaid.x<<3`, `%r1 = %r570 - %rs124`; `%r574 = ctaid.y<<3`, `%r3 = %r574 - %rs125`; `%r2 = %r1 - 1`, `%r6 = %r3 - 1`; `%rs124/%rs125` from `ld.param.v2.u16 [param_0+80]` | s2, s3, s7, s12, s13, s14, s16, s5 |
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| `%rd9` = `param_0` | `mov.b64 %rd9, cuda_dldn_engine_swin_enc4_kernel_param_0` | s1 |
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| shared base `%r11752` | `mov.u32 %r11752, _ZZ33cuda_dldn_engine_swin_enc4_kernel33DldnEngineSwinEncParamsStructBaseE4smem` | s7511 |
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| `%r31615` (second copy) | same `mov.u32` in E62 | s21312 |
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| per-lane weight address | `mul.wide.u32 %rd, %laneid, 16` + `add.s64 %rd, %rd2, %rd` | e.g. s11983–s11984, s12267–s12268 |
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| per-lane *table* address | `shl.b32 %r, %laneid, 2` → `cvt.u64.u32` → `and.b64 %rd, %r, 12` → `add.s64 %rd, %rd74/…, %rd` = `W + ((laneid<<2)&12)` | e.g. s13552–s13555 |
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As in enc0/enc3, a `ld.global.v2.u16` or `ld.global.u32` with that addressing reads
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the **same 16-byte record from the four lanes with equal `laneid&3`**, so those
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tables are indexed by column, not by row.
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The `%tid.z` guard `setp.gt.u32 %p8, %r9, 3; @%p8 bra` at s20–s21 bounds `%tid.z`
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to 0…3 for the whole mma region; the eight phases that stage through shared memory
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(E12→P13…P20) add `(tid.z << 11)` (s11969) resp. `(tid.z << 9)` (s12028) to the
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arena base.
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### 1.2 Constants that survive between epilogues
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| register | first definition | literal | meaning |
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|---|---|---|---|
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| `%f476` | s8077 `mov.f32 %f476, 0f3C8CCB50` | 0.017186790704727173 | f16 `0x2466` = 0.017181396484375 (softmax input scale) |
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| `%fd383` | s8081 `mov.f64 %fd383, 0dBFE1CC0000000000` | −0.55615234375 | f16 clamp lower bound |
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| `%fd385` | s8086 `mov.f64 %fd385, 0d3FE1CC0000000000` | +0.55615234375 | f16 clamp upper bound |
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| `%f478` | s8092 `mov.f32 %f478, 0f3F6D6000` | 0.92724609375 | cubic coefficient |
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| `%f480` | s8097 `mov.f32 %f480, 0f3FB00000` | 1.375 | cubic constant term |
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| `%fd1` | s5976 `mov.f64 %fd1, 0d3F20000000000000` | 2⁻¹³ | norm epsilon |
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| `%f1117` | s13641 `mov.f32 %f1117, 0f3ED306EB` | 0.4121621549129486 | activation coefficient |
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| `%f1118` | s13644 `mov.f32 %f1118, 0f3DA60DD6` | 0.0810810774564743 | activation coefficient |
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| `%f1119` | s13647 `mov.f32 %f1119, 0f3F000000` | 0.5 | activation offset |
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| `%f1120` | s13650 `mov.f32 %f1120, 0f40000000` | 2.0 | activation clamp |
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| `%f1152` | s21429 `mov.f32 %f1152, 0f3F800000` | 1.0 | softmax dividend |
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| `%f1148` | s21606 `mov.f32 %f1148, 0f3E800000` | 0.25 | final output scale |
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`%f1117…%f1120` are defined inside E21 (phase 21's epilogue) and re-materialised
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inside every odd phase's epilogue (E23, E25, … E59, e.g. `s14094–s14100
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cvt.rn.f16.f32 low, %f1117 … %f1120`), exactly as in enc3.
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Live across the whole mma region (defined in the prologue, read by every warp
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reduction):
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| register | statement | value | used as |
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|---|---|---|---|
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| `%r10789` | s7548 | 1 | `shfl.sync.bfly` `b` operand, bit 0 |
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| `%r10798` | s7549 | 2 | `shfl.sync.bfly` `b` operand, bit 1 |
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| `%r10800` | s10280 | −1 | `shfl.sync.bfly` membermask |
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The `c` (clamp/segment) operand of every butterfly is built as
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`%r = (WARP_SZ << 8) - 8192` then `or.b32 %r, %r, 31` (e.g. s10279), i.e. 31 for a
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32-lane warp. The `shfl.sync.down` cascade in E62 uses `%r31545 = 1` (s21424),
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`%r31553 = 8` (s21417) and membermask `%r31555 = -1` (s21510).
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The long-lived **residual vector**: 48 `mov.b32 {%rsA, %rsB}, %r317xx`
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statements (e.g. s5443, s5446 …) split registers produced by
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`cvt.rn.f16x2.e4m3x2 %r31707, %rs128` (s5439) into f16 halves. `%rs128` comes from
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a prologue `ld.global.v2.u16` off the input plane (`param_0+8`, s22–s23). These
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halves are the second addend of the E12 column-table add (§3/E12).
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### 1.3 Quantisation helpers
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* `cvt.rn.satfinite.e4m3x2.f16x2` — the requantisation used everywhere
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(`f16x2_to_e4m3x2_satfinite_bits` in `ptx/lib/zluda_ptx_impl.cpp`).
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* `cvt.rn.f16x2.e4m3x2` — its inverse, used only in the prologue (s5439 ff.).
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* `rcp.approx.ftz.f32`, `rsqrt.approx.ftz.f32`, `ex2.approx.ftz.f32`,
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`div.approx.ftz.f32` — always wrapped as
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`cvt.f32.f16 → op → cvt.rn.f16.f32` (each step rounded through f16).
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### 1.4 The shared arena
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`_ZZ…E4smem` is declared **16384 bytes**. The mma A operands of phases 1…10 come
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from 30 `ld.shared.v4.u32` at `%r11753 = %r11752 + 16*laneid` plus
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`512*k`, `k = 0…29` (s7513–s7542, lines 11835–11864); phases 13…20 come from 8
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such loads at `%r11752 + (tid.z<<9) + 16*laneid + {0,2048,…,14336}` (s12033,
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s12265, s12312, …, s12547); phase 61 comes from 80 `ld.shared.u32`
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(s20242–s21030). The arena is written by the prologue (s7494–s7504), by E12
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(s11986–s12025) and by E60 (s20051–s20215). See §6/U3.
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## 2. Phase table summary
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Reproduced from `rr_layer_spec.py enc4` with `M`, `N`, `K` from `geom()` and
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`check = (M/16)·(N/8)·(K/32)`:
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| # | stmt range | lines | M | N | K | nA | nB | chains | klens | mma | check | =? | weight bytes | C bias bytes | epi |
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| 1 | s7554–s7577 | L11883–12044 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 320..844 | – | 7 |
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| 2 | s7585–s7608 | L12064–12225 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 5440..5964 | – | 7 |
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| 3 | s7616–s7639 | L12245–12406 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 1344..1868 | – | 7 |
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| 4 | s7647–s7670 | L12426–12587 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 6464..6988 | – | 7 |
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| 5 | s7678–s7701 | L12607–12768 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 2368..2892 | – | 7 |
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| 6 | s7709–s7732 | L12788–12949 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 7488..8012 | – | 7 |
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| 7 | s7740–s7763 | L12969–13130 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 3392..3916 | – | 7 |
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| 8 | s7771–s7794 | L13150–13311 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 8512..9036 | – | 7 |
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| 9 | s7802–s7825 | L13331–13492 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 4416..4940 | – | 7 |
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| 10 | s7833–s7856 | L13512–13673 | 96 | 32 | 32 | 6 | 4 | 24 | 1 | 24 | 24 | Y | 9536..10060 | – | 171 |
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| 11 | s8028–s8075 | L14061–14390 | 64 | 96 | 32 | 4 | 12 | 48 | 1 | 48 | 48 | Y | – | 10560..22348 | 3844 |
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| 12 | s11920–s11967 | L24541–24870 | 192 | 96 | 96 | 12 | 12 | 16 | 3 | 48 | 432 | **N** | – | – | 274 |
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| 13 | s12242–s12261 | L25484–25617 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 22848..27468 | – | 27 |
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| 14 | s12289–s12308 | L25675–25808 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 50496..55116 | – | 27 |
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| 15 | s12336–s12355 | L25866–25999 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 78144..82764 | – | 27 |
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| 16 | s12383–s12402 | L26057–26190 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 105792..110412 | – | 27 |
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| 17 | s12430–s12449 | L26248–26381 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 133440..138060 | – | 27 |
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| 18 | s12477–s12496 | L26439–26572 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 161088..165708 | – | 27 |
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| 19 | s12524–s12543 | L26630–26763 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 188736..193356 | – | 27 |
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| 20 | s12571–s12590 | L26821–26954 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 216384..221004 | – | 1029 |
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| 21 | s13620–s13639 | L29419–29552 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 222144..226764 | 227264..227312 | 321 |
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| 22 | s13961–s13980 | L30506–30639 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 227328..231948 | – | 92 |
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| 23 | s14073–s14092 | L30842–30975 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 232768..237388 | 237888..237936 | 172 |
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| 24 | s14265–s14284 | L31538–31671 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 237952..242572 | – | 92 |
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| 25 | s14377–s14396 | L31874–32007 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 243072..247692 | 248192..248240 | 172 |
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| 26 | s14569–s14588 | L32570–32703 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 248256..252876 | – | 92 |
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| 27 | s14681–s14700 | L32906–33039 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 253376..257996 | 258496..258544 | 172 |
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| 28 | s14873–s14892 | L33602–33735 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 258560..263180 | – | 92 |
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| 29 | s14985–s15004 | L33938–34071 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 263680..268300 | 268800..268848 | 172 |
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| 30 | s15177–s15196 | L34634–34767 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 268864..273484 | – | 92 |
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| 31 | s15289–s15308 | L34970–35103 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 273984..278604 | 279104..279152 | 172 |
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| 32 | s15481–s15500 | L35666–35799 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 279168..283788 | – | 92 |
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| 33 | s15593–s15612 | L36002–36135 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 284288..288908 | 289408..289456 | 172 |
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| 34 | s15785–s15804 | L36698–36831 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 289472..294092 | – | 92 |
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| 35 | s15897–s15916 | L37034–37167 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 294592..299212 | 299712..299760 | 172 |
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| 36 | s16089–s16108 | L37730–37863 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 299776..304396 | – | 92 |
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| 37 | s16201–s16220 | L38066–38199 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 304896..309516 | 310016..310064 | 172 |
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| 38 | s16393–s16412 | L38762–38895 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 310080..314700 | – | 92 |
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| 39 | s16505–s16524 | L39098–39231 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 315200..319820 | 320320..320368 | 172 |
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| 40 | s16697–s16716 | L39794–39927 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 320384..325004 | – | 92 |
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| 41 | s16809–s16828 | L40130–40263 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 325504..330124 | 330624..330672 | 172 |
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| 42 | s17001–s17020 | L40826–40959 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 330688..335308 | – | 92 |
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| 43 | s17113–s17132 | L41162–41295 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 335808..340428 | 340928..340976 | 172 |
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| 44 | s17305–s17324 | L41858–41991 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 340992..345612 | – | 92 |
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| 45 | s17417–s17436 | L42194–42327 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 346112..350732 | 351232..351280 | 172 |
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| 46 | s17609–s17628 | L42890–43023 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 351296..355916 | – | 92 |
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| 47 | s17721–s17740 | L43226–43359 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 356416..361036 | 361536..361584 | 172 |
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| 48 | s17913–s17932 | L43922–44055 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 361600..366220 | – | 92 |
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| 49 | s18025–s18044 | L44258–44391 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 366720..371340 | 371840..371888 | 172 |
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| 50 | s18217–s18236 | L44954–45087 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 371904..376524 | – | 92 |
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| 51 | s18329–s18348 | L45290–45423 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 377024..381644 | 382144..382192 | 172 |
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| 52 | s18521–s18540 | L45986–46119 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 382208..386828 | – | 92 |
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| 53 | s18633–s18652 | L46322–46455 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 387328..391948 | 392448..392496 | 172 |
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| 54 | s18825–s18844 | L47018–47151 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 392512..397132 | – | 92 |
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| 55 | s18937–s18956 | L47354–47487 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 397632..402252 | 402752..402800 | 172 |
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| 56 | s19129–s19148 | L48050–48183 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 402816..407436 | – | 92 |
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| 57 | s19241–s19260 | L48386–48519 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 407936..412556 | 413056..413104 | 172 |
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| 58 | s19433–s19452 | L49082–49215 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 413120..417740 | – | 92 |
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| 59 | s19545–s19564 | L49418–49551 | 80 | 160 | 160 | 5 | 20 | 4 | 5 | 20 | 500 | **N** | 418240..422860 | 423360..423408 | 172 |
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| 60 | s19737–s19756 | L50114–50247 | 16 | 160 | 32 | 1 | 20 | 20 | 1 | 20 | 20 | Y | 423424..428044 | – | 1381 |
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| 61 | s21138–s21217 | L51887–52440 | 320 | 640 | 640 | 20 | 80 | 4 | 20 | 80 | 32000 | **N** | 428544..448524 | 530944..530992 | 117 |
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| 62 | s21335–s21344 | L52605–52668 | 80 | 80 | 160 | 5 | 10 | 2 | 5 | 10 | 250 | **N** | 531264..533324 | 533824..533840 | 323 |
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**Arithmetic check.** Rows 1–11, 13–16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36,
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38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58 and 60 satisfy
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`M/16 · N/8 · K/32 == mma`: every A×B tile of the grid is evaluated once and the
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printed `M`/`N`/`K` is the true GEMM shape.
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Rows 12, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55,
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57, 59, 61 and 62 do **not** and are *banded*: only a diagonal band of the M×N
|
||
grid is evaluated, so the printed `M`/`N` are the extents spanned by the fragment
|
||
operands. The chain structure pins the real shape down:
|
||
|
||
* **P12** (`48 mma`, 16 chains of 3): chain `c = 4·(c>>2) + (c&3)` is
|
||
`(A_{3·(c>>2)+k}, B_{2·(c&3)+k})`, `k = 0,1,2` — 4 row tiles × 4 column-pair
|
||
groups, 3 k-steps. Real shape **64×32×96**, all 16 output tiles evaluated.
|
||
(Same as enc0's P6 and enc3's P10.)
|
||
* **P21/23/…/59** (`20 mma`, 4 chains of 5): chain 0 is
|
||
`(A0,B0) (A1,B2) (A2,B4) (A3,B6) (A4,B8)`, chain 1 `(A_j, B_{2j+1})`, chains 2/3
|
||
the same with `B10…B19`. Real shape **80×80×160** with only the 5×2 = 10
|
||
diagonal output tiles of a 5×10 grid evaluated.
|
||
* **P61** (`80 mma`, 4 chains of 20): chain 0 is `(A_j, B_{2j})`, chain 1
|
||
`(A_j, B_{2j+1})`, chains 2/3 with `B_{40+2j}`, `B_{40+2j+1}`, `j = 0…19`.
|
||
Real shape **320×320×640** over 4 output tiles.
|
||
* **P62** (`10 mma`, 2 chains of 5): `(A_j, B_{2j})` / `(A_j, B_{2j+1})`,
|
||
`j = 0…4`. Real shape **80×80×160** over 2 tiles.
|
||
|
||
**Phases that read no weight-image B operand:** **P11** (`Bo = [None, None]` on all
|
||
48 mma; its `B` is a register pack of P9's D, §3/E10) and **P12** (its `B` is
|
||
packed from the `movmatrix` of P10's D, §3/E11). Every other phase loads its `B`
|
||
from `W`.
|
||
|
||
**Weight-image extent.** The largest byte offset used anywhere is 533840 (P62's
|
||
second C seed, `ld.global.u32 [%rd900+533840]`); with the 4-byte read the image is
|
||
**533844 bytes**, 2522 distinct weight-image byte offsets (`weight_image_size`). The single largest
|
||
interior gap is `448524…530944` (the 82 KiB between P61's B block and P61's bias).
|
||
|
||
## 3. The epilogues
|
||
|
||
Phases 1…10 (the stem), 13…59 (the norm + 20 MLP branch pairs) and 60…62 (the
|
||
merge) are highly repetitive; each distinct body is written out once and the
|
||
repeats are tabulated.
|
||
|
||
### E1…E9 — s7578–s7584, s7609–s7615, s7640–s7646, s7671–s7677, s7702–s7708, s7733–s7739, s7764–s7770, s7795–s7801, s7826–s7832: next-B loads
|
||
|
||
Nine identical 7-statement epilogues. Each issues the two `v4.u32` fragments of
|
||
the *next* phase's B operand (`W + 16*laneid + {base, base+512}`):
|
||
|
||
| epilogue | range | loads (statement / line) | offsets | next phase's W block |
|
||
|---|---|---|---|---|
|
||
| E1 | s7578–s7584 | s7582 / L12057, s7584 / L12061 | 5440, 5952 | P2 `5440..5964` |
|
||
| E2 | s7609–s7615 | s7613 / L12238, s7615 / L12242 | 1344, 1856 | P3 `1344..1868` |
|
||
| E3 | s7640–s7646 | s7644 / L12419, s7646 / L12423 | 6464, 6976 | P4 `6464..6988` |
|
||
| E4 | s7671–s7677 | s7675 / L12600, s7677 / L12604 | 2368, 2880 | P5 `2368..2892` |
|
||
| E5 | s7702–s7708 | s7706 / L12781, s7708 / L12785 | 7488, 8000 | P6 `7488..8012` |
|
||
| E6 | s7733–s7739 | s7737 / L12962, s7739 / L12966 | 3392, 3904 | P7 `3392..3916` |
|
||
| E7 | s7764–s7770 | s7768 / L13143, s7770 / L13147 | 8512, 9024 | P8 `8512..9036` |
|
||
| E8 | s7795–s7801 | s7799 / L13324, s7801 / L13328 | 4416, 4928 | P9 `4416..4940` |
|
||
| E9 | s7826–s7832 | s7830 / L13505, s7832 / L13509 | 9536, 10048 | P10 `9536..10060` |
|
||
|
||
**Outputs:** the 8 registers of the next phase's B. Nothing else.
|
||
|
||
### E10 — s7857–s8027: the score-phase bias tiles and the phase-11 operands
|
||
|
||
171 statements: 24 `ld.weak.global.ca.v4.u32` (s7861/L13686 … s7907/L13778), 80
|
||
`cvt.rn.satfinite.e4m3x2.f16x2` (s7908/L13781 … s8026/L14057), 40 `mov.b32`
|
||
(s7910/L13786 … s8027/L14059), 25 `add.s64`, plus the per-lane address pair.
|
||
|
||
1. **Score-bias C seeds** (s7860–s7907): 24 `v4.u32` at
|
||
`W + 16*laneid + 10560 + 512*i`, `i = 0…23` → the 96 `C` operands of phase 11
|
||
(byte block `[10560, 22348]`, 11792 bytes of f16). Phase 11's own mma confirm
|
||
the `4*(n>>1)+m` tile index: for the first A-tile the C offsets run
|
||
`10560, 10568` (s8028, s8029), `12608, 12616` (s8030, s8031), `14656, 14664`,
|
||
`16704, 16712`, `18752, 18760`, `20800, 20808` (s8038, s8039) — i.e.
|
||
`10560 + 2048*(n>>1) + 8*(n&1)` — and the second A-tile starts at `11072`
|
||
(`s8040`) = `10560 + 512`. Structurally identical to enc0's `[8384, 20672)`
|
||
and enc3's `[8448, 20236)`.
|
||
2. **B packs** (s7910–s7979, sources from s7908): the first 24 `mov.b32`
|
||
destinations = phase 11's twelve B fragments (24 b32), each a
|
||
`cvt.rn.satfinite.e4m3x2.f16x2` pair of two registers written by **phase 9's
|
||
mma** (e.g. `s7909: cvt %rs2341, %r7325`, `s7915: cvt %rs2345, %r7335`,
|
||
`s7910: mov.b32 %r8357, {%rs2341, %rs2345}` = B fragment 0).
|
||
3. **A packs** (s7982–s8027): the remaining 16 `mov.b32` destinations
|
||
(`%r8103…%r8106`, `%r8223…%r8226`, `%r8343…%r8346`, `%r8463…%r8466`) = phase
|
||
11's four A fragments (16 b32), also from phase 9's D
|
||
(`s8017: cvt %rs2413, %r7445`, `s8021: mov.b32 %r8463, {%rs2413, %rs2414}`).
|
||
|
||
As in enc3, **fragment 0 of phase 11's A and of its B are bit-identical** (both
|
||
packs read the same two source registers).
|
||
|
||
**Inputs:** phase 9's 48 D registers. **Outputs:** phase 11's 16 A + 24 B
|
||
registers and its 96 C seeds. **Memory:** 24 weight loads only.
|
||
|
||
### E11 — s8076–s11919: the 64×96 score softmax
|
||
|
||
3844 statements, **zero memory access**; byte-for-byte the same code as enc3's E9
|
||
(and enc0's E5) with shifted registers. Histogram: 1048 `mov.b32`, 672
|
||
`cvt.rn.f16.f32`, 384 `cvt.rn.f16.f64`, 192 each `fma.rn.f16x2` /
|
||
`cvt.f32.f16` / `rcp.approx.ftz.f32` / `mul.f16`, 96 each `max.f16x2`/`min.f16x2`/
|
||
`neg.f16x2`/`mul.f16x2`/`and.b32`, 48 `movmatrix`, 16 `shfl.sync.bfly`, 144 packs.
|
||
|
||
| range | statements | what |
|
||
|---|---|---|
|
||
| s8076–s10193 | 2118 | 96 per-element exponent groups |
|
||
| s10194–s10273 | 80 | in-lane partial-sum trees (`add.f16x2`) |
|
||
| s10274–s10408 | 135 | 16 `shfl.sync.bfly.b32` (s10281/L21268 … s10402/L21572) → 8 row sums |
|
||
| s10411–s11172 | 769 | 192 `rcp.approx.ftz.f32` → 96 reciprocals |
|
||
| s11178–s11654 | 477 | 192 `mul.f16` → 96 probabilities |
|
||
| s11656–s11703 | 48 | `movmatrix.sync.trans.aligned.m8n8.b16` of **phase 10's** 48 D registers |
|
||
| s11704–s11918 | 216 | 144 packs |
|
||
|
||
**(a) per-element exponent, s8076–s10193.** Per f16 half `x` of each of phase
|
||
11's 96 D f16x2 registers:
|
||
|
||
```
|
||
m = clamp(f16(x * 0.017181396484375), -0.55615234375, +0.55615234375)
|
||
u = f16(1.375 + m*(0.92724609375 - m^2))
|
||
E = (u_bits << 5) & 0x7FE07FE0 // first: s8102 shl.b32, s8103 and.b32
|
||
```
|
||
|
||
identical to enc0's E5(a): **not** `exp`, and the two `fma.rn.f16x2` at
|
||
s8096/L14453 and s8097 are the cubic, `neg.f16x2` at s8091/L14439 the `−m`.
|
||
|
||
**(b) row sums, s10194–s10408.** In-lane `add.f16x2` tree, then `shfl.sync.bfly`
|
||
over lane bits 0 and 1 (`%r10789 = 1`, `%r10798 = 2`, membermask `%r10800 = −1`),
|
||
then `add.f16x` of the halves and broadcast.
|
||
|
||
**There is no row maximum in this epilogue.** Every `max.f16x2` (96, s8091 …
|
||
s10183) and `min.f16x2` belongs to the clamp of (a); the only shuffles are the 16
|
||
butterflies above.
|
||
|
||
**(c) reciprocity and probability, s10411–s11654.** 192 `rcp.approx.ftz.f32`
|
||
wrapped as `cvt.f32.f16 → rcp → cvt.rn.f16.f32`, then 192 `mul.f16`.
|
||
|
||
**(d) V transpose, s11656–s11703.** Exactly 48 `movmatrix…m8n8.b16` on phase
|
||
**10**'s 48 D registers (`s11656 L23893` … `s11703 L24034`).
|
||
|
||
**(e) packs, s11704–s11918.** 144 packs: the first 24 `mov.b32` → phase 12's 12
|
||
B fragments (the transposed V), the rest → phase 12's 12 A fragments.
|
||
|
||
**Inputs:** phase 11's 96 D, phase 10's 48 D, `%r10789/%r10798/%r10800`.
|
||
**Outputs:** phase 12's 48 A / 24 B registers plus the `%f476`, `%fd383`,
|
||
`%fd385`, `%f478`, `%f480` constants. **Memory:** none.
|
||
|
||
### E12 — s11968–s12241: P·V epilogue — pack, shared staging, residual table, next B/C
|
||
|
||
274 statements. Histogram: `mov.b32`×96, `add.f16`×80,
|
||
`cvt.rn.satfinite.e4m3x2.f16x2`×32, `ld.global.v2.u16`×20, `add.s64`×12,
|
||
`ld.weak.global.ca.v4.u32`×10, `shl.b32`×5, `add.s32`×4, `mov.u32`×4,
|
||
`st.shared.v4.u32`×4, `bar.sync`×2, `bra`×1, `ld.shared.v4.u32`×1,
|
||
`mul.wide.u32`×1, `cvt.u64.u32`×1, `and.b64`×1.
|
||
|
||
**(a) require and shared staging, s11969–s12025.**
|
||
|
||
```
|
||
s11969 L24877: shl.b32 %r12002, %r9, 11 // tid.z << 11
|
||
s11970 L24878: add.s32 %r12003, %r11752, %r12002
|
||
s11973 L24883: add.s32 %r12005, %r12003, %r12004 // + 16*laneid
|
||
s11986 L24912: st.shared.v4.u32 [%r12005], {%r12009, %r12008, %r12007, %r12006}
|
||
```
|
||
|
||
32 packs of phase 12's D → 16 b32 (96 `mov.b32` in the whole epilogue; the other
|
||
80 pair the table adds) stored one `v4.u32` each at `+0`, `+512`, `+1024`, `+1536`
|
||
(s11986, s11999, s12012, s12025).
|
||
|
||
**(b) `bar.sync 0` (s12026) and skip guard.** `s12027 L25001: @%p8 bra
|
||
$L__BB1_422` with `%p8 = (tid.z > 3)` (s20–s21) — phases 13…20 are only run for
|
||
`tid.z ≤ 3`.
|
||
|
||
**(c) staging read-back, s12028–s12033.** `%r29518 = %r11752 + (tid.z<<9) +
|
||
(laneid<<4)` (s12028–s12032), `ld.shared.v4.u32 [%r29518]` → `%r29519 … %r29522` =
|
||
**phase 13's A operand** (one 16-byte fragment, `nA = 1`).
|
||
|
||
**(d) next B, s12034–s12056.** 10 `v4.u32` at `W + 16*laneid + 22848 + 512*j`,
|
||
`j = 0..9` → phase 13's 20 B fragments (block `[22848, 27468)`).
|
||
|
||
**(e) residual column table, s12062–s12081.** 20 `ld.global.v2.u16` at
|
||
`W + ((laneid<<2)&12) + {221504 + 16*i}`, `i = 0…19` → 40 f16 covering the 160
|
||
columns of phase 13's output.
|
||
|
||
**(f) residual add, s12082–s12241.** 80 `add.f16` — two per f16x2 — each
|
||
`table[column] + <half of the long-lived prologue residual>`:
|
||
|
||
```
|
||
s12084 L25089: add.f16 %rs3965,%rs6450,%rs3967 // %rs6450 = W+221504, %rs3967 = residual
|
||
s12083 L25085: add.f16 %rs3968,%rs6451,%rs3970
|
||
s12085 L25092: mov.b32 %r12073, {%rs3965, %rs3968}
|
||
```
|
||
|
||
The 40 results `%r12073 …` are **phase 13's C operands**. The residual halves are
|
||
`%r31707`, `%r31706`, … split at s5443 ff. (§1.2).
|
||
|
||
**Inputs:** phase 12's D, the shared staging, `W`. **Outputs:** phase 13's A
|
||
(4 regs), B (40 regs) and C (40 regs).
|
||
|
||
### E13…E19 — s12262–s12288, s12309–s12335, s12356–s12382, s12403–s12429, s12450–s12476, s12497–s12523, s12544–s12570: next-A from shared, next-B from W
|
||
|
||
Seven identical 27-statement epilogues (`add.s64`×11, 10 `v4.u32`, `mov.u32`×2,
|
||
`shl.b32`, `add.s32`, 1 `ld.shared.v4.u32`, `mul.wide.u32`):
|
||
|
||
```
|
||
s12264 L25627: add.s32 %r29525, %r29516, %r29524 // %r29516 = %r11752 + (tid.z<<9)
|
||
s12265 L25628: ld.shared.v4.u32 {…}, [%r29525+2048]
|
||
s12267 L25632: mul.wide.u32 %rd648, %r12266, 16
|
||
s12268 L25633: add.s64 %rd649, %rd2, %rd648
|
||
```
|
||
|
||
| epilogue | range | shared read offset | becomes | B offsets (10 loads) | next phase's W block |
|
||
|---|---|---|---|---|---|
|
||
| E13 | s12262–s12288 | s12265, `+2048` | P14 A | 50496 … 55104 | P14 `50496..55116` |
|
||
| E14 | s12309–s12335 | s12312, `+4096` | P15 A | 78144 … 82752 | P15 `78144..82764` |
|
||
| E15 | s12356–s12382 | s12359, `+6144` | P16 A | 105792 … 110400 | P16 `105792..110412` |
|
||
| E16 | s12403–s12429 | s12406, `+8192` | P17 A | 133440 … 138048 | P17 `133440..138060` |
|
||
| E17 | s12450–s12476 | s12453, `+10240` | P18 A | 161088 … 165696 | P18 `161088..165708` |
|
||
| E18 | s12497–s12523 | s12500, `+12288` | P19 A | 188736 … 193344 | P19 `188736..193356` |
|
||
| E19 | s12544–s12570 | s12547, `+14336` | P20 A | 216384 … 220992 | P20 `216384..221004` |
|
||
|
||
### E20 — s12591–s13619: the RMS norm before the MLP
|
||
|
||
1029 statements: 302 `mov.b32`, 240 `mul.f16`, 82 `add.f16`, 80 `cvt.f32.f16`,
|
||
80 `rsqrt.approx.ftz.f32`, 80 `cvt.rn.f16.f32`, 42 `add.f16x2`, 4
|
||
`shfl.sync.bfly`, 40 packs, 20 `ld.global.v2.u16`, 10 weight `v4.u32`, 4
|
||
`ld.global.u32`.
|
||
|
||
| range | what |
|
||
|---|---|
|
||
| s12594–s12751 | 80 `mul.f16` — squares of phase 20's 40 D f16x2 |
|
||
| s12753–s12817 | 42 `add.f16x2` — in-lane reduction, with the 4 `shfl.sync.bfly` over lane bits 0,1 at s12795/L27521, s12801, s12810, s12816/L27575 |
|
||
| s12819–s12940 | 82 `add.f16` — `+ 2⁻¹³` (`%fd1`, s5976) broadcast into the f16x2 pairs |
|
||
| s12946–s13259 | 80 `rsqrt.approx.ftz.f32` (s12946/L27961 … s13259/L28469) |
|
||
| s13268–s13287 | 20 `ld.global.v2.u16` gain at `W + ((laneid<<2)&12) + {221824 + 16*i}` (`s13289 mul.f16 %rs4692,%rs4693,%rs6490` with `%rs6490 = W+221824`) |
|
||
| s13289–s13407 | 80 `mul.f16` — `inv · gain` |
|
||
| s13408–s13526 | 80 `mul.f16` — `x · (inv·gain)` (`s13408 mul.f16 %rs4935,%rs5217,%rs4695`) |
|
||
| s13532–s13550 | 10 weight `v4.u32` = phase 21's B (`222144 + 512*j`) |
|
||
| s13556–s13559 | 4 `ld.global.u32` at `W + ((laneid<<2)&12) + {227264,227280,227296,227312}` = phase 21's C bias |
|
||
| s13560–s13618 | 40 packs of the normalised values → phase 21's A |
|
||
|
||
**What it computes.** The same per-**row** RMS reduction as enc3's E14, over the
|
||
**160** columns of a M=16/N=160 tile: the lane's 20 one-per-n-tile partials for
|
||
each of its two rows are tree-summed in-lane, the four `t = laneid&3` lanes are
|
||
folded with two butterfly steps, the f16x2 halves are added, then
|
||
|
||
```
|
||
inv = f16(rsqrt.approx(f32(f16(sumsq + 2^-13))))
|
||
out[row,c] = x[row,c] · inv · gain[c]
|
||
```
|
||
|
||
There is no mean subtraction and no `1/N`. The 80 `rsqrt` results are the two row
|
||
sums re-emitted once per (row, n-tile) pair, not 80 distinct sums (the half-copies
|
||
that feed them are duplicates, e.g. `s12818`-range `add.f16 … , %rs…, %rs…` with
|
||
identical addends). `gain[c]` is per column.
|
||
|
||
**Outputs:** phase 21's B (40 regs) and C (4 regs), 20 packed A registers, and the
|
||
normalised f16x2 registers that E21/E22 re-read.
|
||
|
||
### E21 — s13640–s13960: clamped cubic activation + column bias + pack
|
||
|
||
321 statements: `add.f16`×80, `mov.b32`×76, `cvt.rn.f16.f32`×32, `mul.f16x2`×24,
|
||
20 `ld.global.v2.u16`, 10 weight `v4.u32`, 8 each `neg/max/min/abs/sub/add.f16x2`,
|
||
8 packs, `mov.f32`×4.
|
||
|
||
**(a) constants and activation, s13641–s13780.** Eight groups; each materialises
|
||
the activation constants (`s13641 L29561: mov.f32 %f1117, 0f3ED306EB`, `s13644
|
||
%f1118, 0f3DA60DD6`, `s13647 %f1119, 0f3F000000`, `s13650 %f1120, 0f40000000`)
|
||
and then, on **phase 21's D**,
|
||
|
||
```
|
||
y = clamp(x, -2, +2) // s13653 neg, s13654 max, s13655 min
|
||
g = 0.5 + y*(0.412109375 - 0.0810546875*|y|) // abs, mul, sub, mul, add
|
||
out = x * g // s13661 mul.f16x2
|
||
```
|
||
|
||
The same cubic ramp as enc0's E13 / enc3's E15 — **not** a sigmoid, GELU or SiLU.
|
||
|
||
**(b) column bias, s13809–s13948.** 20 `ld.global.v2.u16` at
|
||
`W + ((laneid<<2)&12) + {232464 + 16*i}` then 80 `add.f16`, e.g.
|
||
`s13932 L30428: add.f16 %rs5416,%rs6524,%rs5418` — the second addend is a half of
|
||
phase **20**'s D (a residual). The 40 results `%r14926 … %r14956` are **phase
|
||
22's C operand**.
|
||
|
||
**(c) pack, s13949–s13959.** 8 packs of the **activation outputs**
|
||
(`s13949 L30478: cvt.rn.satfinite.e4m3x2.f16x2 %rs5453, %r14617`) → phase 22's A
|
||
fragment.
|
||
|
||
**(d) next B, s13785–s13803.** 10 `v4.u32` at `227328 + 512*j` → phase 22's B.
|
||
|
||
**No stores and no `ld.global` beyond the two tables.**
|
||
|
||
### E22 / E24 / … / E58 — s13981–s14072 and its 19 repeats: next B/C loads + pack
|
||
|
||
92 statements, identical shape, for every even phase 22…58:
|
||
|
||
```
|
||
s13984 L30650: add.s64 %rd263, %rd676, 232768
|
||
s13985 L30652: ld.weak.global.ca.v4.u32 { %r14958,…},[%rd263] // 232768 + 512*j, 10 loads
|
||
s14009 L30697: ld.global.u32 %r…, [%rd…+237888] // C bias, 4 words at +16*i
|
||
s14013 L30702: cvt.rn.satfinite.e4m3x2.f16x2 %rs…, %r… // 40 packs
|
||
s14015 L30707: mov.b32 %r…, {%rs…, %rs…} // 20 b32 = 5 A fragments
|
||
```
|
||
|
||
The 40 pack sources (`%r28751 %r28752 %r28753 …`, `s14013 L30702: cvt %rs5461,
|
||
%r28752`) are the **normalised values** E20 produced with the second of its
|
||
multi-sets, i.e. phase 23's A operand is the *same* normed tile phase 21's A was
|
||
built from — phases 21 and 23 are two parallel GEMMs off one normed tile, each
|
||
with its own weight block and bias. The 4 C words are
|
||
`W + ((laneid<<2)&12) + {bias_base + 16*i}` (`s13556 L29274:
|
||
ld.global.u32 %r14283, [%rd669+227264]`, `s13557`/`s13558`/`s13559`) and each is
|
||
used in **both halves** of the *next odd* phase's mma C operand: for the P23 bias
|
||
loaded by E22, `s14073 C={%r15048,%r15048}` with `[%r15048=W+237888]`,
|
||
`s14074 C={%r15058,%r15058}` with `W+237904`.
|
||
|
||
| epilogue | range | next-B block | next-C bytes |
|
||
|---|---|---|---|
|
||
| E22 | s13981–s14072 | 232768..237388 | 237888..237936 |
|
||
| E24 | s14285–s14376 | 243072..247692 | 248192..248240 |
|
||
| E26 | s14589–s14680 | 253376..257996 | 258496..258544 |
|
||
| E28 | s14893–s14984 | 263680..268300 | 268800..268848 |
|
||
| E30 | s15197–s15288 | 273984..278604 | 279104..279152 |
|
||
| E32 | s15501–s15592 | 284288..288908 | 289408..289456 |
|
||
| E34 | s15805–s15896 | 294592..299212 | 299712..299760 |
|
||
| E36 | s16109–s16200 | 304896..309516 | 310016..310064 |
|
||
| E38 | s16413–s16504 | 315200..319820 | 320320..320368 |
|
||
| E40 | s16717–s16808 | 325504..330124 | 330624..330672 |
|
||
| E42 | s17021–s17112 | 335808..340428 | 340928..340976 |
|
||
| E44 | s17325–s17416 | 346112..350732 | 351232..351280 |
|
||
| E46 | s17629–s17720 | 356416..361036 | 361536..361584 |
|
||
| E48 | s17933–s18024 | 366720..371340 | 371840..371888 |
|
||
| E50 | s18237–s18328 | 377024..381644 | 382144..382192 |
|
||
| E52 | s18541–s18632 | 387328..391948 | 392448..392496 |
|
||
| E54 | s18845–s18936 | 397632..402252 | 402752..402800 |
|
||
| E56 | s19149–s19240 | 407936..412556 | 413056..413104 |
|
||
| E58 | s19453–s19544 | 418240..422860 | 423360..423408 |
|
||
|
||
### E23 / E25 / … / E59 — s14093–s14264 and its 18 repeats: clamped cubic activation + pack
|
||
|
||
172 statements; identical op mix to E21 minus the table loads and the `mov.f32`
|
||
block (36 `mov.b32`, 32 `cvt.rn.f16.f32`, 24 `mul.f16x2`, 8 each
|
||
`neg/max/min/abs/sub/add.f16x2`, 10 weight `v4.u32`, 8 packs):
|
||
|
||
```
|
||
s14094 L30986: cvt.rn.f16.f32 low, %f1117
|
||
s14102 L31009: neg.f16x2 %r15244,%r15243
|
||
s14109 L31037: add.f16x2 %r15250,%r15243,%r15249
|
||
s14234 L31471: ld.weak.global.ca.v4.u32 { …},[%rd…] // next B, 10 loads
|
||
s14253 L31510: cvt.rn.satfinite.e4m3x2.f16x2 … // 8 packs of activation outputs
|
||
```
|
||
|
||
Same function as E21(a) on the odd phase's D, 8 packs of the activation *outputs*
|
||
→ the next even phase's A, and 10 weight loads → its B. **No column bias, no
|
||
`ld.global`.** The 18 repeats are at s14093, s14377, s14681, s14985, s15289,
|
||
s15593, s15897, s16201, s16505, s16809, s17113, s17417, s17721, s18025, s18329,
|
||
s18637, s18937, s19241, s19545 (phases 23…59 odd).
|
||
|
||
#### Shape of the attention + MLP region, E12–E60
|
||
|
||
```
|
||
P11 A = pack(P9.D) B = pack(P9.D) C = bias@10560+512i → scores 64×96
|
||
E11: cubic-exponent softmax (no row max), 48 movmatrix(P10.D) + packs
|
||
P12 A = pack(scores) B = pack(transpose(P10.D)) C = 0 → 64×32
|
||
E12: pack → shared slot, read back as P13 A; table@221504 + residual → P13 C
|
||
P13 A = shared, B = W@22848, C = table+residual → D13
|
||
E13: shared slot +2048 → P14 A; load P14 B
|
||
P14…P19 the same for the shared slots +4096 …, +14336
|
||
P20 A = shared, B = W@216384, C = D19 → D20 (16×160)
|
||
E20: row-RMS norm over 160 columns (+2^-13, rsqrt, gain@221824), pack → P21 A
|
||
P21 A = normed tile, B = W@222144, C = bias@227264 → D21 (banded 80×80×160)
|
||
E21: cubic activation(D21); table@232464 + D20 → P22 C; pack → P22 A
|
||
P22 A = pack(activation), B = W@232768, C = D20+table → D22
|
||
E22: pack of the *normed* tile → P23 A; load P23 B and C
|
||
P23 A = normed tile, B = W@237952, C = bias@237888 → D23
|
||
… the P21/P22 pair then repeats 19 more times (P23/P24 … P59/P60).
|
||
P60 A = pack(activation P59), B = W@423424, C = D58 → D60 (16×160)
|
||
E60: arena scatter, shared staging, next B/C
|
||
P61 A = 20 shared slots, B = W@428544, C = bias@530944 → 4×20 k-steps
|
||
E61: pack + scatter to param+56, next B/C
|
||
P62 A = pack(E61), B = W@531264, C = bias@533824 → D62
|
||
E62: the final epilogue
|
||
```
|
||
|
||
### E60 — s19757–s21137: pack → plane-arena scatter → shared staging → next B/C
|
||
|
||
1381 statements. Histogram: `add.s32`×218, `or.b32`×129, `shl.b32`×99,
|
||
`and.b32`×80, `ld.shared.u32`×80, `mul.wide.u16`×69, `add.s64`×66, `shr.u32`×51,
|
||
`setp.lt.s32`×44, `bra`×41, `$label`×41, `cvt.rn.satfinite.e4m3x2.f16x2`×40,
|
||
`selp.b32`×40, `ld.weak.global.ca.v4.u32`×40, `mov.b32`×20, `st.shared.u32`×20,
|
||
`st.global.u32`×20, `bar.sync`×2, `ld.global.u32`×4.
|
||
|
||
**(a) packs, s19757–s19816.** 40 `cvt.rn.satfinite.e4m3x2.f16x2` + 20 `mov.b32`
|
||
→ `%r371 … %r390` = phase 60's 16×160 output as 20 b32 = 40 e4m3 per lane.
|
||
|
||
**(b) plane-arena scatter, s19817–s20029.** `%rd5 = cvta(ld.param.u64 [%rd1+-32])`
|
||
(s19817–s19818; `%rd1 = param_0+80` ⇒ **`param_0+48`**), lane decomposition
|
||
`s20035 shr %r424, laneid, 2` (`g`), `s20036 and %r425, laneid, 3` (`t`), and 20
|
||
guarded `st.global.u32` (`s19843 L50422: st.global.u32 [%rd810], %r371` …
|
||
`s20029 L50646: … %r390`), each preceded by a
|
||
`setp.lt.s32 %p, idx, 0` + `bra` guard. The index is built from
|
||
`(%r1 + ((g+8j)&7))`, `((tid.z<<1) + ((g+8j)>>3))` and `(%r425 | 4)` in the same
|
||
way as enc3's E46(b) (§6/U4).
|
||
|
||
**(c) shared staging, s20033–s20215.** `bar.sync 0`, then 20 `st.shared.u32` at
|
||
`%r29635 = %r11752 + (idx<<2)` with
|
||
`idx = t | ((laneid&28) | (y<<5))`, `y = (tid.z<<1) + (laneid>>5)`
|
||
(`s20051 L50672: st.shared.u32 [%r29635], %r371`), then the `+512*j` variants.
|
||
|
||
**(d) staging read-back, s20222–s21030.** `bar.sync 0` (s20220), then 80
|
||
`ld.shared.u32` at `%r11752 + (idx2<<2)` with
|
||
`idx2 = ((laneid<<1)&24) | ((laneid<<2)&0xFFFFFFC0) | (laneid&3)`
|
||
(`s20234–s20241`) plus byte offsets `{0, 1024, …, 7168}` and the `+16` variants
|
||
(`s20242 L50905: ld.shared.u32 …`). These 80 values are **phase 61's 20 A
|
||
fragments**. `ld.param.v2.u32 [%rd940+-80]` at s20222 re-reads `param_0+0`.
|
||
|
||
**(e) next B/C, s21039–s21137.** Inside the loop `$L__BB1_406` (s21041),
|
||
`s21039 add.s64 %rd7, %rd947, 428544`, `s21042: mul.lo.s32 %r31250, %r31708, 640`
|
||
then 40 `v4.u32` at `W + 16*laneid + 428544 + 640*%r31708 + 512*j`, `j = 0…39`
|
||
(`s21048–s21126`) = phase 61's 80 B fragments, and 4 `ld.global.u32` at
|
||
`W + ((laneid<<2)&12) + {530944, 530960, 530976, 530992}` (s21134–s21137) =
|
||
phase 61's C bias.
|
||
|
||
**Outputs:** `%r371…%r390` (read again by (c)), phase 61's A/B/C.
|
||
The shared arena is re-used four times in this epilogue — `%r11752` appears as the
|
||
base of the E60 stores and of the P61 read-back.
|
||
|
||
### E61 — s21218–s21334: pack → surface scatter → next B/C
|
||
|
||
117 statements: 8 packs + 2 `mov.b32` (s21218–s21227), 4 guarded stores to
|
||
**`param_0+56`** (s21257 `st.global.v2.u16`, s21267 `st.global.u32`,
|
||
s21298 `st.global.u32`, s21306 `st.global.v2.u16`), 5 `bra`, then 5 weight
|
||
`v4.u32` (s21319–s21327) and 2 `ld.global.u32` (s21333–s21334).
|
||
|
||
```
|
||
s21253 L52499: setp.lt.s32 %p381, %r545, 0
|
||
s21254 L52500: @%p381 bra $L__BB1_408
|
||
s21255 L52502: mul.wide.s32 %rd898, %r545, 4
|
||
s21257 L52504: st.global.v2.u16 [%rd899], {%rs6698, %rs6699}
|
||
```
|
||
|
||
The destination is `param+56` (`%rd6 = cvta(%rd849)`, `%rd849 = ld.param.u64
|
||
[%rd945+-24]`, s21037–s21038), **not** the plane arena; the extents are
|
||
`param_0+0`, halved (`s20223 shr %r451, %r29720, 1` = `ey>>1`, `s20224 shr %r452,
|
||
%r29719, 1` = `ex>>1`, `s20225 shl %r453, %r452, 3` = the row stride). The index
|
||
bases use `%r536 = %r1>>1` (s21036) and `%r535 = %r3>>1` (s21033).
|
||
|
||
Then phase 62's B (5 `v4.u32` at `531264 + 512*j`) and C (2 `ld.global.u32` at
|
||
`533824`, `533840`).
|
||
|
||
### E62 — s21345–s21667: the final epilogue
|
||
|
||
323 statements: 4 `st.shared.u32` (s21357–s21374), 2 `bar.sync`, 5 `ld.shared.u32`
|
||
(s21414–s21422), `mul.ftz.f32`/`ex2.approx`/`add.ftz.f32`/`div.approx`×12,
|
||
12 `fma.rn.f16x2`, 4 `shfl.sync.down.b32`, 9 `tex.base.2d.v4.f16.s32`
|
||
(s21526–s21585), 3 `sust.b.2d.v4.b16.zero` (s21649, s21650, s21665).
|
||
|
||
**(a) shared staging, s21345–s21374.**
|
||
|
||
```
|
||
s21348 L52679: and.b32 %r557, %r31392, 3 // t
|
||
s21350 L52681: shl.b32 %r558, %r31608, 4 // %r31608 = tid.z
|
||
s21351 L52682: add.s32 %r31395, %r556, %r558 // g + (tid.z<<4)
|
||
s21354 L52685: mad.lo.s32 %r31398, %r31397, 6, %r557
|
||
s21357 L52688: st.shared.u32 [%r559], %r31372
|
||
```
|
||
|
||
Phase 62's D (`%r31372/%r31382` and `%r31392`-group counterparts) is written to
|
||
`%r31615 + 4*(6*index + t)` with a `%r560 > 5` guard on the second word.
|
||
|
||
**(b) row max and softmax, s21387–s21613.** After `bar.sync 0` (s21387),
|
||
`%r31565 = smem + 4*(6*%r562 + 48*%r563)` (s21410–s21413) and
|
||
`s21414–s21422` read a **6-element row** (`ld.shared.u32 [%r31565] … [+20]`); then
|
||
|
||
```
|
||
max.f16x2 / max.f16 over the row // row maximum
|
||
sub.f16x2 x - rowmax // e.g. s21502-region
|
||
mul.ftz.f32 by log2(e), ex2.approx.ftz.f32 // 2^((x-max)*log2e)
|
||
div.approx.ftz.f32 1.0(rowsum) with %f1152 = 0f3F800000 (s21429)
|
||
mul.f16x2 p = e / rowsum
|
||
```
|
||
|
||
**This epilogue has a real row maximum** (unlike E11), and a true `2^u` `ex2`
|
||
rather than the cubic mantissa trick.
|
||
|
||
**(c) texture gather, s21421–s21590.** One texture (`load.param.u64 [%rd943+8]` at
|
||
s21524, copied into `%rd916 … %rd932`, s21525–s21572) with 9
|
||
`tex.base.2d.v4.f16.s32` reads forming a 3×3 stencil; the 8 neighbour coordinates
|
||
are clamped by `selp` chains with `1` as the out-of-range sentinel (the same
|
||
pattern as enc3's E48(c)). Each texel is weighted by one of the five softmax
|
||
values with `fma.rn.f16x2` (`s21530 L52979`, `s21547 L53007`, …,
|
||
`s21580 L53074`) and one extra texel is folded in with `fma.rn.f16`.
|
||
|
||
**(d) second sigmoid, difference, cross-lane sum, s21591–s21648.** Three
|
||
`mul.f16` + `sub.f16` products and differences, `%f1148 = 0.25` (s21606), then the
|
||
`shfl.sync.down` cascade: delta `1` (`%r31545`, s21424) and `8` (`%r31553`,
|
||
s21417), membermask `%r31555 = -1` (s21510), clamp operand `(WARP_SZ<<8)-8192 | 31`
|
||
(s21619, s21625, s21632, s21641), each followed by `add.f16x2` / `add.f16`.
|
||
|
||
**(e) surface stores, s21646–s21667.**
|
||
|
||
```
|
||
s21646 L53255: ld.param.u64 %rd936, [%rd943+40]
|
||
s21647 L53256: ld.param.u64 %rd938, [%rd943+48]
|
||
s21649 L53259: sust.b.2d.v4.b16.zero [%rd934, {%r31559,%r565}], {%rs6803,%rs6806,%rs6809,%rs6840}
|
||
s21650 L53262: sust.b.2d.v4.b16.zero [%rd936, {%r31559,%r565}], {%rs6794,%rs6797,%rs6800,%rs6841}
|
||
s21665 L53280: sust.b.2d.v4.b16.zero [%rd938, {%r31587,%r31588}], {%rs6842,%rs6843,%rs6827,%rs6845}
|
||
```
|
||
|
||
Three 4-channel b16 surface writes. The handles are `param_0+32` (`%rd934`, read
|
||
at s21421), `+40` and `+48`; the texel source is the texture at `param_0+8`
|
||
(s21524). The third store is guarded (`s21655 … bra`) and stores `0` in its
|
||
fourth channel as in enc3.
|
||
|
||
**Inputs:** phase 62's D, the shared staging of (a), `param+0/+8/+32/+40/+48`.
|
||
**Outputs:** none (the kernel `ret`s at s21667 / L53284).
|
||
|
||
## 4. The plane-arena and surface writes
|
||
|
||
`param_0+48` is reached once (`s19817 ld.param.u64 %rd808, [%rd1+-32]` with
|
||
`%rd1 = param_0+80` at s4) and is never the base of an `ld.*` in this entry. The
|
||
complete set of global writes in the 21667-statement entry:
|
||
|
||
* **E60, 20 × `st.global.u32 [%rd5 + 4*idx], v`** — s19843, s19852, s19885, s19893,
|
||
s19902, s19910, s19919, s19927, s19936, s19944, s19953, s19961, s19970, s19978,
|
||
s19987, s19995, s20004, s20012, s20021, s20029 (§3/E60(b)). Value: phase 60's
|
||
requantised 16×160 output, 20 b32 per lane.
|
||
* **E61, 4 stores to `param_0+56`** — s21257 (`v2.u16`), s21267 (`u32`),
|
||
s21298 (`u32`), s21306 (`v2.u16`).
|
||
* **E62, 3 `sust.b.2d.v4.b16.zero`** — s21649, s21650, s21665.
|
||
|
||
Nothing else writes to global memory.
|
||
|
||
## 5. Uncharacterised
|
||
|
||
**U1. The identity of the 11792-byte score bias (P11's C operand).** Phase 11
|
||
adds the f16 table `[10560, 22348]` indexed as
|
||
`byte = 10560 + 512*(4*(n>>1) + m) + 16*laneid + 8*(n&1)`. Whether it is a
|
||
relative position bias, a learned score bias or a per-lane constant cannot be
|
||
decided from the PTX. *Missing:* the weight image's layout description (the
|
||
`_prep` permutation).
|
||
|
||
**U2. The identity of the per-column tables.** `W+221504` (E12's C seed add),
|
||
`W+221824` (E20's norm gain), `W+232464` (E21's post-activation add) and
|
||
`W+227264`/`227264+65536`… (the odd phases' GEMM bias) all use the
|
||
`W + ((laneid<<2)&12) + off` pattern. Their role is computable (§3) but their
|
||
model names are not.
|
||
|
||
**U3. The shared-arena layout.** The arena (16384 bytes) is written by the
|
||
prologue (s7494–s7504), E12 (s11986–s12025) and E60 (s20051–s20215), and read by
|
||
P1–P10 (s7513–s7542, at `%r11752 + 16*laneid + 512*k` with **no** `tid.z` term),
|
||
P13–P20 (s12033, s12265, …, s12547, at `%r11752 + (tid.z<<9) + 16*laneid + 2048*j`)
|
||
and P61 (s20242–s21030). The prologue's store side and the E60 store side add
|
||
`tid.z` terms that the P1–P10 read side does not, so the mapping cannot be
|
||
reconstructed from the PTX alone. *Missing:* the launch's `%tid.z`/`ctaid`
|
||
ranges, or a memory dump.
|
||
|
||
**U4. E60's / E61's index algebra.** E60(b)'s arena stores, E60(c)'s shared
|
||
stores and E61's `param+56` stores each form index bases from
|
||
`(laneid&28) | (y<<5)` and `((g+8)<<2)&28 | (y2<<5)` plus `+512*j`, with
|
||
`y = (tid.z<<1) + (laneid>>5)` and `y2 = (tid.z<<1) + ((g+8)>>3)`, while E60(d)'s
|
||
read side uses `16*g + t` and `16*g + t + 128`. I could not prove the
|
||
store↔load permutation, nor whether the `%r31708` loop (s21041, `+128` at s21308)
|
||
runs once or twice per `tid.z` (the guard `%r31708 > 159` at s20227/s21046 is
|
||
checked before the first body, exactly as in enc3). *Missing:* a plane-arena dump.
|
||
|
||
**U5. The MLP block's shape.** §3 establishes, from the pack sources and each
|
||
phase's C operand, that the MLP region is: one normed tile feeding every *odd*
|
||
phase (P21, P23, …, P59) as its `A`, each odd phase's activation feeding its
|
||
*paired* even phase as `A`, and the even phases' `C` chaining
|
||
(`D22 = … + D20 + table@232464`, `D24 = … + D22`, …, verified from each even
|
||
phase's C operands tracing to the previous even phase's mma). Only the **first**
|
||
even phase adds the column table `@232464` to the residual
|
||
(`s13932 add.f16 %rs5416,%rs6524,%rs5418`); every later even phase's `C` is the
|
||
previous even phase's `D` alone. Whether the 20 pairs are one wide MLP, a stack
|
||
of residual blocks, or something else is a model-level question the PTX cannot
|
||
answer. *Missing:* the model source.
|
||
|
||
**U6. The stem's shift structure.** Phases 1…10 read the same 30 shared A
|
||
fragments in five shift groups (P1/P2 at `+0/512/…`, P3/P4 at `+512/…`, P5/P6 at
|
||
`+1024/…`, P7/P8 at `+1536/…`, P9/P10 at `+2048/…`, s7513–s7542) and accumulate
|
||
in two chains (`P1→P3→P5→P7→P9` and `P2→P4→P6→P8→P10`; each phase's C operands name
|
||
the previous one's D, e.g. `s7616 C={%r5574,%r5575}` = P1's D). Whether that is a
|
||
2×2 / 5-tap stencil is a property of the high-level model. *Missing:* the model
|
||
source. (enc3 has four shift groups and eight phases, so the tap count is a
|
||
per-stage constant.)
|
||
|
||
**U7. The meaning of the prologue residual vector.** §1.2 tracks the f16 halves
|
||
`%rs…` back through `cvt.rn.f16x2.e4m3x2 %r31707, %rs128` (s5439) to the input
|
||
plane at `param_0+8` (s22–s23). What that plane holds is not determinable from
|
||
the PTX.
|
||
|
||
**U8. The logical meaning of E62's final expression.** The tail computes
|
||
`out = (acc − sigmoid(acc)) * 0.25` on three channels gathered by texture from a
|
||
3×3 stencil. The arithmetic is exact in §3/E62(d); what model term it corresponds
|
||
to is not derivable. (Same gap as enc0 §6/U6.)
|
||
|
||
**U9. The 82 KiB hole in the weight image.** Between P61's B block
|
||
(`428544..448524`) and P61's bias (`530944`) there are 82420 bytes that no phase
|
||
in this entry reads. Whether that region is padding, is unused by this stage, or
|
||
belongs to another kernel's parameters cannot be told from this entry.
|
||
*Missing:* the `_prep` code that builds the image.
|
||
|
||
## 6. Quick acceptance index
|
||
|
||
| requirement | where |
|
||
|---|---|
|
||
| every phase's M/N/K with the arithmetic checked | §2 (rows flagged **N** are banded; the real shapes are derived there) |
|
||
| weight image extent | §2 (533844 bytes, max offset 533840) |
|
||
| phases that read no weight operand | §2 (P11, P12) |
|
||
| score epilogue: row max? | **none** — §3/E11 (16 `shfl.sync.bfly`, no maximum) |
|
||
| score bias operand | §3/E10 (24 `v4.u32` at `W+10560+512*i`, indexed `4*(n>>1)+m`) |
|
||
| attention Q/K/V | §3/E10 (P11 A and B both from P9's D), §3/E11(d) (P10's D transposed) |
|
||
| the norm | §3/E20 (row RMS over 160 columns, `+2^-13`, `rsqrt.approx`, gain) |
|
||
| the activations | §3/E21, §3/E23 (clamped cubic ramp, 8 groups per phase) |
|
||
| patch merge | §3/E60 (arena + shared staging), §3/E61 (`param+56`), §3/E62 (textures + surfaces) |
|
||
| per-launch plane-arena writes | §4 |
|