WP40 RAID: Phase 3 gate — primitives benchmark records, summary, figure; status/progress updated · 3905e5b · wp40_uqo

WP40 RAID: Phase 3 gate — primitives benchmark records, summary, figure; status/progress updated

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Simon-Pierre Boucher committed yesterday (Nov 2, 2026) parent 5aa6672 Browse files

8 changed files +5,287 −8

modified RESEARCH_STATUS.md +7 −8

				`@@ -1,6 +1,6 @@`
1	# RESEARCH_STATUS.md — RAID (UQO WP 40)	1	# RESEARCH_STATUS.md — RAID (UQO WP 40)
2		2
3	−Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending ·	3	+Last update: 2026-11-02 (Phase 3 passed). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending ·
4	🧭 experimental · ⛔ blocked · ⏳ planned · ✖ not implemented (deliberately).	4	🧭 experimental · ⛔ blocked · ⏳ planned · ✖ not implemented (deliberately).
5		5
6	## Phases	6	## Phases
				`@@ -9,7 +9,7 @@ Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifact`
9	\| 0 Audit \| scope & feasibility memo \| ✅ passed 2026-11-02 \| `docs/audit.md`, `docs/capabilities.md`, `docs/novelty_matrix.md`, `docs/risks.md`, `docs/PROGRESS.md` \|	9	\| 0 Audit \| scope & feasibility memo \| ✅ passed 2026-11-02 \| `docs/audit.md`, `docs/capabilities.md`, `docs/novelty_matrix.md`, `docs/risks.md`, `docs/PROGRESS.md` \|
10	\| 1 Foundation \| clean build + tests + docs \| ✅ passed 2026-11-02 \| `ctest` 26/26 (314 assertions), `pytest` 7/7, `docs/PROGRESS.md` Phase 1 \|	10	\| 1 Foundation \| clean build + tests + docs \| ✅ passed 2026-11-02 \| `ctest` 26/26 (314 assertions), `pytest` 7/7, `docs/PROGRESS.md` Phase 1 \|
11	\| 2 Data \| offline synthetic tests + opt-in live tests \| ✅ passed 2026-11-02 \| offline `[findata]` 4/4, live `[live]` 2/2 (60 assertions), `docs/operations/findata.md` \|	11	\| 2 Data \| offline synthetic tests + opt-in live tests \| ✅ passed 2026-11-02 \| offline `[findata]` 4/4, live `[live]` 2/2 (60 assertions), `docs/operations/findata.md` \|
12	−\| 3 Numerical primitives \| accuracy + measured break-even \| ⏳ \| — \|	12	+\| 3 Numerical primitives \| accuracy + measured break-even \| ✅ passed 2026-11-02 \| `[metal]` 6 cases / 6 411 assertions; `experiments/results/bench_primitives_summary.json` (Metal wins: fused realized ≥ 39 k elements up to 3.4×, GARCH NLL P=64 up to 7.9×; CPU wins: rolling sums, GARCH P=1, small panels) \|
13	\| 4 Econometrics (Tier A) \| references + Monte Carlo \| ⏳ \| — \|	13	\| 4 Econometrics (Tier A) \| references + Monte Carlo \| ⏳ \| — \|
14	\| 5 Extensions (Tier B) \| per-feature specs + tests \| ⏳ \| — \|	14	\| 5 Extensions (Tier B) \| per-feature specs + tests \| ⏳ \| — \|
15	\| 6 Benchmarking E1–E7 \| every claim traceable \| ⏳ \| — \|	15	\| 6 Benchmarking E1–E7 \| every claim traceable \| ⏳ \| — \|
				`@@ -20,10 +20,10 @@ Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifact`
20	\| Method \| Tier \| CPU FP64 \| Metal FP32 \| Reference software \| Status \|	20	\| Method \| Tier \| CPU FP64 \| Metal FP32 \| Reference software \| Status \|
21	\|---\|---\|---\|---\|---\|---\|	21	\|---\|---\|---\|---\|---\|---\|
22	\| returns (log/arith), lag/lead, rolling windows, calendar-aware aggregation \| A \| ✅ \| ⏳ (Phase 3) \| numpy; exchange_calendars (calendar exact 2000–2026) \| ✅ CPU \|	22	\| returns (log/arith), lag/lead, rolling windows, calendar-aware aggregation \| A \| ✅ \| ⏳ (Phase 3) \| numpy; exchange_calendars (calendar exact 2000–2026) \| ✅ CPU \|
23	−\| RV, BPV, RSV±, RQ, jump proxy, TriPV, rCov/rCorr \| A \| ✅ (numpy truth 1e−12) \| ⏳ (Phase 3) \| highfrequency 1.0.3 (R comparison Phase 4) \| ✅ CPU \|	23	+\| RV, BPV, RSV±, RQ, jump proxy, TriPV, rCov/rCorr \| A \| ✅ (numpy truth 1e−12) \| ✅ fused kernel 1e−6 vs FP64 \| highfrequency 1.0.3 (R comparison Phase 4) \| ✅ CPU \|
24	−\| OLS/WLS/ridge, HC0–3, HAC, cluster, rolling OLS \| A \| ✅ (statsmodels 1e−9) \| ⏳ (sufficient stats, Phase 3) \| statsmodels 0.15, scipy 1.18 \| ✅ CPU \|	24	+\| OLS/WLS/ridge, HC0–3, HAC, cluster, rolling OLS \| A \| ✅ (statsmodels 1e−9) \| ✅ sufficient statistics 1e−6 (k ≤ 8) \| statsmodels 0.15, scipy 1.18 \| ✅ CPU \|
25	\| HAR-RV, log-HAR, HAR-X, HARQ \| A \| ⏳ \| ⏳ \| highfrequency `HARmodel`, statsmodels \| ⏳ \|	25	\| HAR-RV, log-HAR, HAR-X, HARQ \| A \| ⏳ \| ⏳ \| highfrequency `HARmodel`, statsmodels \| ⏳ \|
26	−\| GARCH(1,1), GJR, EGARCH (N, t), QMLE/Hessian/OPG SE, forecasts \| A \| ✅ (arch 8.0: loglik 5e−4, params 5 %) \| ⏳ (batched likelihood, Phase 3) \| arch 8.0 ✅, rugarch 1.5.6 (Phase 4) \| ✅ CPU \|	26	+\| GARCH(1,1), GJR, EGARCH (N, t), QMLE/Hessian/OPG SE, forecasts \| A \| ✅ (arch 8.0: loglik 5e−4, params 5 %) \| ✅ batched NLL 2e−5 (grids) \| arch 8.0 ✅, rugarch 1.5.6 (Phase 4) \| ✅ CPU \|
27	\| Bootstrap (stationary / circular block), Monte Carlo \| A \| ⏳ \| ⏳ \| arch.bootstrap \| ⏳ \|	27	\| Bootstrap (stationary / circular block), Monte Carlo \| A \| ⏳ \| ⏳ \| arch.bootstrap \| ⏳ \|
28	\| VAR, GFEVD, Diebold–Yilmaz \| B \| ⏳ \| ⏳ \| statsmodels VAR \| ⏳ \|	28	\| VAR, GFEVD, Diebold–Yilmaz \| B \| ⏳ \| ⏳ \| statsmodels VAR \| ⏳ \|
29	\| Realized GARCH, HEAVY, DCC, PCA/shrinkage, Kalman \| B \| ✖ until Tier A passes \| \| \| ⏳ \|	29	\| Realized GARCH, HEAVY, DCC, PCA/shrinkage, Kalman \| B \| ✖ until Tier A passes \| \| \| ⏳ \|
				`@@ -35,6 +35,5 @@ Last update: 2026-11-02 (Phase 2 passed). Legend: ✅ verified by tests/artifact`
35	not tested unless they come back.	35	not tested unless they come back.
36		36
37	## Next safe action	37	## Next safe action
38	−Phase 3: Metal backend (device discovery, runtime + prebuilt shader library, buffer pool, batched reductions,	38	+Phase 4: HAR family (fit, rolling, batched via GPU sufficient statistics), block bootstrap, R references
39	−rolling sums, regression sufficient statistics, GARCH likelihood batch), FP32-vs-FP64 accuracy tests, first break-even	39	+(highfrequency / rugarch), Monte Carlo (bias/RMSE/coverage), gradient checks, registry completion.
40	−microbenchmarks (bench_reductions) with manifests.

modified docs/PROGRESS.md +39 −0

+ Gate evidence: offline tests in `ctest`; live run transcript above; no vendor data in git (`scripts/check_no_secrets.sh`).
+ Open: least-privilege key for benchmarks (needs `findata create-key` on M3U96a — owner action, optional).
++
++## Phase 3 — Numerical primitives (2026-11-02, 15:40–16:30 ET) — GATE PASSED
++Plan: Metal backend with FP32 "double-float" (error-free-transform) accumulation, fused realized kernel, rolling sums,
++regression sufficient statistics, batched GARCH likelihood; CPU/GPU agreement tests; measured break-even analysis.
++
++Executed:
++- `backends/metal/shaders/raid_kernels.metal` (TwoSum/Fast2Sum double-float, deterministic threadgroup tree reductions,
++  chunked partial sums combined in FP64 on the CPU) and `backends/metal/host/metal_backend.mm` (device discovery,
++  prebuilt `raid.metallib` with runtime-MSL fallback, pipeline cache, buffer pool by power-of-two size class, GPU
++  timing from `GPUStartTime/GPUEndTime`, `-fno-fast-math` / `fastMathEnabled = NO` so the compensation is not optimised
++  away). Metal has no `lgamma`/`log1p`: Student-t constants are computed in FP64 on the host and passed per parameter
++  vector.
++- Tests `[metal]` (6 cases, 6 411 assertions): fused and single-statistic accumulators vs CPU FP64 within 1e−6
++  (Σx⁴ 1e−5) for n = 390/3 900/39 000 across chunk boundaries (4 096); bitwise determinism across runs; rolling sums
++  1e−5; regression statistics 1e−6 (and the solve from GPU statistics agrees with CPU QR to 1e−5); batched GARCH NLL
++  2e−5 relative (GJR + Student-t fixed ν 5e−5), argmin over a 16-point grid identical; +inf on invalid parameters.
++  Full suite: `ctest` 38/38 (2 live skipped), `pytest` 7/7.
++- `bench_bench_primitives` (laptop M5 Max 40-core GPU, 18 CPU threads, load ≈ 3–4 from other sessions, no thermal
++  warning, 5 repetitions, shuffled order, 2 warm-ups; raw records `experiments/results/raw/bench_primitives.jsonl`
++  + manifest; summary `experiments/results/bench_primitives_summary.{json,csv}`, figure
++  `fig_bench_primitives_throughput.pdf`). Medians of wall-clock including FP64→FP32 conversion and buffer traffic;
++  verdicts use non-overlapping bootstrap 95 % CIs of the median:
++  - realized_fused: Metal wins from 39 000 elements (100 × 390: 2.4×), 2.0–3.4× vs 18-thread CPU at 3.9 M–39 M
++    elements (max 3.4× at 1 000 × 39 000); ties at 390 000 for 10 × 39 000 and 100 × 3 900 shapes; CPU 1 thread is
++    27–40× slower than Metal at 39 M.
++  - regression_stats (k = 4): break-even ≈ 390 000 elements for a single long series (3.9×); ties for most shapes
++    between 390 k and 3.9 M; 1.1–1.4× at 39 M. CPU wins below 39 000 elements.
++  - rolling_sumsq (w = 22, direct O(w) kernel): **CPU wins at every size** (Metal 0.4–0.9× of CPU-MT); the GPU kernel
++    is memory/arithmetic-bound by its O(w) design and the CPU running sum is O(1) per element — a negative result kept
++    for the paper (a scan-based kernel is future work).
++  - garch_nll: with one parameter vector per series (P = 1) the **CPU wins everywhere** (0.01–0.33×; the recursion is
++    sequential and the GPU is launch-bound); with P = 64 parameter vectors per series Metal wins from 100 series
++    (1.9×) up to 7.9× at 1 000 × 3 900 — batched likelihood evaluation is where the GPU pays off.
++  - Device time is 5–20× smaller than wall time for the reductions: FP64→FP32 conversion and buffer fills dominate
++    ("unified memory is not free computation"); E6 will add the FP32-resident ablation.
++  - Shader library: prebuilt metallib loaded in 0.23 ms; first kernel call 14 ms (pipeline creation); runtime MSL
++    compilation of the bundle is measured separately in E7 (toolchain-less nodes).
++
++Gate evidence: accuracy tests and the measured break-even table above; no claim beyond the tested shapes.

added experiments/results/bench_primitives_summary.csv +208 −0

++kernel,S,n,elements,backend,threads,median_s,ci_lo,ci_hi,device_s,elements_per_s,reps,precision,peak_rss_mb
++garch_nll_P1,1,390,390,cpu,1,1.7909333109855652e-06,1.7499551177024841e-06,1.8328428268432617e-06,0.0,217763552.44929796,5,fp64,3255.451648
++garch_nll_P1,1,390,390,cpu,18,1.7499551177024841e-06,1.6670674085617065e-06,1.8333084881305695e-06,0.0,222862858.62692922,5,fp64,3368.943616
++garch_nll_P1,1,390,390,metal,0,0.0009180000051856041,0.00044724997133016586,0.0009358339011669159,0.00032679166179150343,424836.59890736995,5,fp32,2962.440192
++garch_nll_P1,1,3900,3900,cpu,1,1.6250181943178177e-05,1.6207806766033173e-05,1.637497916817665e-05,0.0,239997312.86930108,5,fp64,2962.440192
++garch_nll_P1,1,3900,3900,cpu,18,1.695798709988594e-05,1.691700890660286e-05,1.9416213035583496e-05,0.0,229980125.41395503,5,fp64,3431.858176
++garch_nll_P1,1,3900,3900,metal,0,0.001348957885056734,0.0010095001198351383,0.0015331669710576534,0.0011987084290012717,2891120.6518771155,5,fp32,2962.440192
++garch_nll_P1,10,390,3900,cpu,1,2.1916814148426056e-05,2.1541956812143326e-05,7.208297029137611e-05,0.0,177945570.62847915,5,fp64,2962.440192
++garch_nll_P1,10,390,3900,cpu,18,2.929195761680603e-05,1.7000362277030945e-05,4.200031980872154e-05,0.0,133142347.50095384,5,fp64,2962.440192
++garch_nll_P1,10,390,3900,metal,0,0.0003432091325521469,0.0003193751908838749,0.0009956671856343746,0.00019762502051889896,11363333.98531415,5,fp32,2920.169472
++garch_nll_P1,10,3900,39000,cpu,1,0.0002155420370399952,0.00016279099509119987,0.00037720799446105957,0.0,180939182.60948467,5,fp64,576.782336
++garch_nll_P1,10,3900,39000,cpu,18,6.916606798768044e-05,6.245775148272514e-05,7.533328607678413e-05,0.0,563860302.2358668,5,fp64,781.43488
++garch_nll_P1,10,3900,39000,metal,0,0.0014300826005637646,0.0012115412391722202,0.0016847080551087856,0.0010766249615699053,27271152.019208886,5,fp32,3360.11264
++garch_nll_P1,100,390,39000,cpu,1,0.0001916671171784401,0.0001916252076625824,0.0002199173904955387,0.0,203477782.59580857,5,fp64,3431.87456
++garch_nll_P1,100,390,39000,cpu,18,0.00016116676852107048,0.00015066703781485558,0.00017320923507213593,0.0,241985369.30335766,5,fp64,3359.932416
++garch_nll_P1,100,390,39000,metal,0,0.0006238752976059914,0.0006115422584116459,0.0006384579464793205,0.0004310833755880594,62512492.720348835,5,fp32,3355.901952
++garch_nll_P1,100,3900,390000,cpu,1,0.0016154590994119644,0.0016071251593530178,0.0016200002282857895,0.0,241417439.87326083,5,fp64,3222.339584
++garch_nll_P1,100,3900,390000,cpu,18,0.00020695803686976433,0.00020262505859136581,0.0002222089096903801,0.0,1884439985.5098226,5,fp64,2962.440192
++garch_nll_P1,100,3900,390000,metal,0,0.0016493331640958786,0.0015722080133855343,0.004429208114743233,0.0009533748961985111,236459199.68740082,5,fp32,2962.440192
++garch_nll_P1,1000,390,390000,cpu,1,0.0016390001401305199,0.001627500168979168,0.0016581248492002487,0.0,237949949.14945084,5,fp64,3359.932416
++garch_nll_P1,1000,390,390000,cpu,18,0.0002765827812254429,0.00027295900508761406,0.00033191684633493423,0.0,1410066086.8042636,5,fp64,2962.440192
++garch_nll_P1,1000,390,390000,metal,0,0.0011531668715178967,0.0010962923988699913,0.0011774590238928795,0.00017799995839595795,338199101.65009224,5,fp32,3222.339584
++garch_nll_P1,1000,3900,3900000,cpu,1,0.018310166895389557,0.01771716633811593,0.019527375232428312,0.0,212996420.09172553,5,fp64,572.112896
++garch_nll_P1,1000,3900,3900000,cpu,18,0.0014978330582380295,0.001383374910801649,0.0015932917594909668,0.0,2603761466.306366,5,fp64,3432.742912
++garch_nll_P1,1000,3900,3900000,metal,0,0.0072068748995661736,0.007158916909247637,0.009398084133863449,0.0010924999369308352,541149951.171591,5,fp32,3360.11264
++garch_nll_P1,10000,390,3900000,cpu,1,0.017741417046636343,0.01734916679561138,0.017816499806940556,0.0,219824605.3146817,5,fp64,3355.901952
++garch_nll_P1,10000,390,3900000,cpu,18,0.0022433330304920673,0.002103041857481003,0.002292540855705738,0.0,1738484632.905596,5,fp64,2962.440192
++garch_nll_P1,10000,390,3900000,metal,0,0.00675466563552618,0.006540417205542326,0.007071124855428934,0.00046787504106760025,577378690.5880197,5,fp32,2962.440192
++garch_nll_P1,10000,3900,39000000,cpu,1,0.16226391727104783,0.16133012529462576,0.16484179068356752,0.0,240349183.3298581,5,fp64,3255.451648
++garch_nll_P1,10000,3900,39000000,cpu,18,0.01383341709151864,0.012941500172019005,0.014138792175799608,0.0,2819260038.3538756,5,fp64,3254.272
++garch_nll_P1,10000,3900,39000000,metal,0,0.06106641702353954,0.05950908316299319,0.0616582497023046,0.004054000019095838,638648899.0334327,5,fp32,3355.901952
++garch_nll_P64,1,390,390,cpu,1,8.287513628602028e-05,8.27503390610218e-05,8.458364754915237e-05,0.0,4705874.614239238,5,fp64,577.159168
++garch_nll_P64,1,390,390,cpu,18,0.00017224997282028198,0.00012754183262586594,0.0002139592543244362,0.0,2264151.3006617934,5,fp64,3431.514112
++garch_nll_P64,1,390,390,metal,0,0.0005012080073356628,0.00047737499698996544,0.0006123748607933521,0.0003255000337958336,778120.0505418383,5,fp32,3431.46496
++garch_nll_P64,1,3900,3900,cpu,1,0.0008078329265117645,0.0008031250908970833,0.0008203750476241112,0.0,4827730.923076213,5,fp64,3431.87456
++garch_nll_P64,1,3900,3900,cpu,18,0.00014187488704919815,0.000135000329464674,0.00021779071539640427,0.0,27489008.668937948,5,fp64,3222.339584
++garch_nll_P64,1,3900,3900,metal,0,0.0014235423877835274,0.00134983379393816,0.0033927499316632748,0.00122337497305125,2739644.4485733556,5,fp32,3431.87456
++garch_nll_P64,10,390,3900,cpu,1,0.0008257082663476467,0.000809917226433754,0.0008320827037096024,0.0,4723217.8227436915,5,fp64,3432.742912
++garch_nll_P64,10,390,3900,cpu,18,0.0002438751980662346,0.00013074977323412895,0.0002598753198981285,0.0,15991786.089460358,5,fp64,3368.943616
++garch_nll_P64,10,390,3900,metal,0,0.0010179998353123665,0.0004632081836462021,0.0010751672089099884,0.00032300001475960016,3831041.877136759,5,fp32,3431.530496
++garch_nll_P64,10,3900,39000,cpu,1,0.008083874825388193,0.008056249935179949,0.00812424998730421,0.0,4824419.086440666,5,fp64,3355.901952
++garch_nll_P64,10,3900,39000,cpu,18,0.000775500200688839,0.0006874999962747097,0.0008766250684857368,0.0,50290122.38211957,5,fp64,3432.742912
++garch_nll_P64,10,3900,39000,metal,0,0.0013822498731315136,0.0008970410563051701,0.0033571659587323666,0.0006641249638050795,28214869.654243305,5,fp32,3431.530496
++garch_nll_P64,100,390,39000,cpu,1,0.008346542250365019,0.008285791147500277,0.008543540723621845,0.0,4672593.611839012,5,fp64,3431.514112
++garch_nll_P64,100,390,39000,cpu,18,0.001005750149488449,0.0009415419772267342,0.0010966667905449867,0.0,38777026.30204572,5,fp64,781.484032
++garch_nll_P64,100,390,39000,metal,0,0.0005332920700311661,0.0005230000242590904,0.0005429168231785297,0.00033650000113993883,73130658.02332444,5,fp32,2962.440192
++garch_nll_P64,100,3900,390000,cpu,1,0.0801338329911232,0.07999316696077585,0.08033083425834775,0.0,4866858.172667244,5,fp64,3359.932416
++garch_nll_P64,100,3900,390000,cpu,18,0.006173874717205763,0.005890249740332365,0.006268457975238562,0.0,63169406.22606451,5,fp64,3432.742912
++garch_nll_P64,100,3900,390000,metal,0,0.0021704169921576977,0.0018634586594998837,0.0022297906689345837,0.0010580417001619935,179688972.86059555,5,fp32,3431.858176
++garch_nll_P64,1000,390,390000,cpu,1,0.09679854195564985,0.08949454175308347,0.10223195794969797,0.0,4028986.306205791,5,fp64,2962.440192
++garch_nll_P64,1000,390,390000,cpu,18,0.00848708301782608,0.008417499717324972,0.008939292281866074,0.0,45952183.94598623,5,fp64,2962.440192
++garch_nll_P64,1000,390,390000,metal,0,0.002336665987968445,0.002312499564141035,0.0027117920108139515,0.001452916651032865,166904470.73228282,5,fp32,3359.932416
++garch_nll_P64,1000,3900,3900000,cpu,1,0.8561791670508683,0.8505779169499874,0.9446879159659147,0.0,4555121.34619399,5,fp64,2962.440192
++garch_nll_P64,1000,3900,3900000,cpu,18,0.08150566695258021,0.0744811249896884,0.10778554202988744,0.0,47849433.61384933,5,fp64,3255.451648
++garch_nll_P64,1000,3900,3900000,metal,0,0.010272707790136337,0.009604125283658504,0.010956583078950644,0.0029698750004172325,379646737.7125929,5,fp32,2962.440192
++realized_fused,1,390,390,cpu,1,1.4998950064182281e-06,1.416075974702835e-06,4.041939973831177e-06,0.0,260018200.16144055,5,fp64,2962.440192
++realized_fused,1,390,390,cpu,18,1.4998950064182281e-06,1.4579854905605316e-06,1.6670674085617065e-06,0.0,260018200.16144055,5,fp64,2962.440192
++realized_fused,1,390,390,metal,0,0.0002344171516597271,0.00019499985501170158,0.00025337468832731247,3.199989441782236e-05,1663700.7882687368,5,fp32,3432.742912
++realized_fused,1,3900,3900,cpu,1,1.1624768376350403e-05,1.1375173926353455e-05,1.2792181223630905e-05,0.0,335490555.4879026,5,fp64,2962.440192
++realized_fused,1,3900,3900,cpu,18,1.116609200835228e-05,1.1124648153781891e-05,1.2124888598918915e-05,0.0,349271705.5423496,5,fp64,3432.742912
++realized_fused,1,3900,3900,metal,0,0.0006333747878670692,0.0001420830376446247,0.000777125358581543,2.037500962615013e-05,6157491.7011356,5,fp32,2913.878016
++realized_fused,1,39000,39000,cpu,1,0.00018258299678564072,0.0001637078821659088,0.00037499982863664627,0.0,213601489.11230472,5,fp64,2962.440192
++realized_fused,1,39000,39000,cpu,18,0.0001671668142080307,0.00015920819714665413,0.00017870916053652763,0.0,233299893.79032168,5,fp64,2962.440192
++realized_fused,1,39000,39000,metal,0,0.000206624623388052,0.0001971670426428318,0.00024229194968938828,4.3874955736100674e-05,188748075.42543435,5,fp32,3355.901952
++realized_fused,1,390000,390000,cpu,1,0.002032375428825617,0.002019832842051983,0.002052249852567911,0.0,191893679.91196227,5,fp64,3222.339584
++realized_fused,1,390000,390000,cpu,18,0.0020858747884631157,0.002067000139504671,0.0027133747935295105,0.0,186971913.25053322,5,fp64,2962.440192
++realized_fused,1,390000,390000,metal,0,0.0009353337809443474,0.00017445813864469528,0.0009425836615264416,1.2583332136273384e-05,416963449.78178984,5,fp32,781.1072
++realized_fused,10,390,3900,cpu,1,1.1292286217212677e-05,1.1167023330926895e-05,1.2415926903486252e-05,0.0,345368504.214433,5,fp64,3432.742912
++realized_fused,10,390,3900,cpu,18,0.00014200014993548393,0.0001277080737054348,0.0001649591140449047,0.0,27464759.732802525,5,fp64,577.175552
++realized_fused,10,390,3900,metal,0,0.0002327919937670231,0.00019591627642512321,0.0002467092126607895,3.124994691461325e-05,16753153.477877328,5,fp32,3255.451648
++realized_fused,10,3900,39000,cpu,1,0.00018791621550917625,0.00017224997282028198,0.00020966678857803345,0.0,207539300.929012,5,fp64,3431.858176
++realized_fused,10,3900,39000,cpu,18,0.000135000329464674,0.00012287497520446777,0.0001421659253537655,0.0,288888183.86332357,5,fp64,3360.096256
++realized_fused,10,3900,39000,metal,0,0.00016404176130890846,0.00015954114496707916,0.0009339582175016403,1.6249949112534523e-05,237744338.32467064,5,fp32,3222.339584
++realized_fused,10,39000,390000,cpu,1,0.002572625409811735,0.0020360001362860203,0.0035845423117280006,0.0,151596108.2062624,5,fp64,2962.440192
++realized_fused,10,39000,390000,cpu,18,0.00036349985748529434,0.00035787513479590416,0.00039070891216397285,0.0,1072902759.0217906,5,fp64,3369.04192
++realized_fused,10,39000,390000,metal,0,0.0007184999994933605,0.000268666073679924,0.0007987502031028271,5.52500132471323e-05,542797495.1635388,5,fp32,3355.901952
++realized_fused,10,390000,3900000,cpu,1,0.02089220890775323,0.020823125261813402,0.021495667286217213,0.0,186672458.48535842,5,fp64,3431.497728
++realized_fused,10,390000,3900000,cpu,18,0.0025267917662858963,0.0025061247870326042,0.0027628750540316105,0.0,1543459200.7289019,5,fp64,3431.858176
++realized_fused,10,390000,3900000,metal,0,0.0010219174437224865,0.001003749668598175,0.0010474580340087414,8.649996016174555e-05,3816355248.6134977,5,fp32,3222.339584
++realized_fused,100,390,39000,cpu,1,0.0001871250569820404,0.00016624992713332176,0.00021525006741285324,0.0,208416770.2016683,5,fp64,2962.440192
++realized_fused,100,390,39000,cpu,18,0.0005520828999578953,0.0004998329095542431,0.0005905842408537865,0.0,70641564.88631389,5,fp64,3431.530496
++realized_fused,100,390,39000,metal,0,0.00022633420303463936,0.00017816666513681412,0.00027566729113459587,3.15000070258975e-05,172311561.73966,5,fp32,3368.943616
++realized_fused,100,3900,390000,cpu,1,0.002043417189270258,0.0020072502084076405,0.0020909998565912247,0.0,190856767.7945766,5,fp64,3432.742912
++realized_fused,100,3900,390000,cpu,18,0.0006015831604599953,0.0005330839194357395,0.0006621670909225941,0.0,648289423.0313727,5,fp64,3355.8528
++realized_fused,100,3900,390000,metal,0,0.0006413329392671585,0.000292791984975338,0.0008833748288452625,5.287490785121918e-05,608108481.7593294,5,fp32,490.962944
++realized_fused,100,39000,3900000,cpu,1,0.020590624772012234,0.020551583264023066,0.020679709035903215,0.0,189406588.83265492,5,fp64,3222.339584
++realized_fused,100,39000,3900000,cpu,18,0.0021904585883021355,0.001996333710849285,0.002361500170081854,0.0,1780449089.8971806,5,fp64,2962.440192
++realized_fused,100,39000,3900000,metal,0,0.0011692089028656483,0.0008370000869035721,0.0011960407719016075,0.000259208376519382,3335588696.289753,5,fp32,3360.096256
++realized_fused,100,390000,39000000,cpu,1,0.2325868341140449,0.2128961249254644,0.24819900002330542,0.0,167679310.60481706,5,fp64,2962.440192
++realized_fused,100,390000,39000000,cpu,18,0.01879258267581463,0.016645667143166065,0.02031658310443163,0.0,2075286865.7159925,5,fp64,2962.440192
++realized_fused,100,390000,39000000,metal,0,0.008720249868929386,0.007397250272333622,0.008947291877120733,0.0021910000359639525,4472348910.43187,5,fp32,486.178816
++realized_fused,1000,390,390000,cpu,1,0.002235791180282831,0.0021259579807519913,0.003065959084779024,0.0,174434895.10083154,5,fp64,2962.440192
++realized_fused,1000,390,390000,cpu,18,0.0008399169892072678,0.0007132496684789658,0.0009002499282360077,0.0,464331600.6360231,5,fp64,3355.8528
++realized_fused,1000,390,390000,metal,0,0.00033845799043774605,0.00033012498170137405,0.00035137496888637543,0.00013987498823553324,1152284806.4410944,5,fp32,3431.87456
++realized_fused,1000,3900,3900000,cpu,1,0.021244540810585022,0.021230708342045546,0.021389917004853487,0.0,183576573.14282066,5,fp64,3431.530496
++realized_fused,1000,3900,3900000,cpu,18,0.0017422502860426903,0.0017107920721173286,0.0017863749526441097,0.0,2238484350.522551,5,fp64,3431.46496
++realized_fused,1000,3900,3900000,metal,0,0.0008750832639634609,0.0008294158615171909,0.0015468327328562737,0.0002547500189393759,4456718761.065055,5,fp32,3432.742912
++realized_fused,1000,39000,39000000,cpu,1,0.23877166723832488,0.21975037455558777,0.2514020833186805,0.0,163335962.13939813,5,fp64,2962.440192
++realized_fused,1000,39000,39000000,cpu,18,0.02024729223921895,0.019154875073581934,0.029473000206053257,0.0,1926183488.5979028,5,fp64,2962.440192
++realized_fused,1000,39000,39000000,metal,0,0.005891874898225069,0.005617166869342327,0.00844891695305705,0.0009469999931752682,6619285146.693929,5,fp32,3369.04192
++realized_fused,10000,390,3900000,cpu,1,0.021238334011286497,0.020878124982118607,0.021370540838688612,0.0,183630222.49897087,5,fp64,3431.858176
++realized_fused,10000,390,3900000,cpu,18,0.002125917002558708,0.0019880831241607666,0.002400666009634733,0.0,1834502473.6647966,5,fp64,2962.440192
++realized_fused,10000,390,3900000,metal,0,0.0022132499143481255,0.0018930002115666866,0.0032122922129929066,0.001203041640110314,1762114605.6380522,5,fp32,3431.87456
++realized_fused,10000,3900,39000000,cpu,1,0.2336724577471614,0.22654250031337142,0.24493679078295827,0.0,166900285.87878695,5,fp64,2962.440192
++realized_fused,10000,3900,39000000,cpu,18,0.01569391693919897,0.015392750035971403,0.01590104214847088,0.0,2485039276.7524476,5,fp64,3432.742912
++realized_fused,10000,3900,39000000,metal,0,0.0078027499839663506,0.006132957991212606,0.008690916933119297,0.0019207500154152513,4998237811.046104,5,fp32,577.1264
++regression_stats,1,390,390,cpu,1,3.1669624149799347e-06,3.125052899122238e-06,3.2088719308376312e-06,0.0,123146393.57741508,5,fp64,2962.440192
++regression_stats,1,390,390,cpu,18,3.2088719308376312e-06,3.2079406082630157e-06,3.3332034945487976e-06,0.0,121538038.41532433,5,fp64,2962.440192
++regression_stats,1,390,390,metal,0,0.000894167460501194,0.00017508305609226227,0.000988542102277279,7.087492849677801e-05,436159.91100973333,5,fp32,3368.910848
++regression_stats,1,3900,3900,cpu,1,2.9958784580230713e-05,2.950010821223259e-05,3.0708033591508865e-05,0.0,130178845.859239,5,fp64,3368.894464
++regression_stats,1,3900,3900,cpu,18,3.0207913368940353e-05,3.008265048265457e-05,3.0375085771083832e-05,0.0,129105243.13175379,5,fp64,2962.440192
++regression_stats,1,3900,3900,metal,0,0.0003482499159872532,0.0003069578669965267,0.0003833337686955929,0.00019212497863918543,11198854.101497471,5,fp32,2962.440192
++regression_stats,1,39000,39000,cpu,1,0.00030233291909098625,0.00030054105445742607,0.0003049168735742569,0.0,128996869.13770398,5,fp64,2962.440192
++regression_stats,1,39000,39000,cpu,18,0.0003838753327727318,0.0003343336284160614,0.0006159590557217598,0.0,101595483.4042161,5,fp64,578.486272
++regression_stats,1,39000,39000,metal,0,0.0004085828550159931,0.0003508748486638069,0.00041229184716939926,0.00018866662867367268,95451875.96888623,5,fp32,3359.932416
++regression_stats,1,390000,390000,cpu,1,0.0029733749106526375,0.002949208952486515,0.0029905838891863823,0.0,131164085.16220291,5,fp64,3368.943616
++regression_stats,1,390000,390000,cpu,18,0.0030428748577833176,0.0030017499811947346,0.003628334030508995,0.0,128168267.9136231,5,fp64,572.112896
++regression_stats,1,390000,390000,metal,0,0.0007901252247393131,0.0007615000940859318,0.0008232500404119492,9.650003630667925e-05,493592645.5564979,5,fp32,2920.12032
++regression_stats,10,390,3900,cpu,1,3.1250063329935074e-05,3.095809370279312e-05,4.149973392486572e-05,0.0,124799747.08608383,5,fp64,2920.185856
++regression_stats,10,390,3900,cpu,18,4.133302718400955e-05,2.475036308169365e-05,4.3540727347135544e-05,0.0,94355537.58590388,5,fp64,3359.932416
++regression_stats,10,390,3900,metal,0,0.0006523327901959419,0.0003105420619249344,0.0007279999554157257,9.250000584870577e-05,5978543.557236411,5,fp32,2962.440192
++regression_stats,10,3900,39000,cpu,1,0.0002997498959302902,0.0002982090227305889,0.000300500076264143,0.0,130108468.85855077,5,fp64,2962.440192
++regression_stats,10,3900,39000,cpu,18,7.625017315149307e-05,7.187481969594955e-05,8.49580392241478e-05,0.0,511474248.3602653,5,fp64,3432.742912
++regression_stats,10,3900,39000,metal,0,0.00036174990236759186,0.0003430834040045738,0.0005066245794296265,0.00018737500067800283,107809289.63560627,5,fp32,3431.514112
++regression_stats,10,39000,390000,cpu,1,0.003083667252212763,0.0030186669901013374,0.003116208128631115,0.0,126472789.73441304,5,fp64,3431.530496
++regression_stats,10,39000,390000,cpu,18,0.0005624173209071159,0.0005049579776823521,0.0006032092496752739,0.0,693435257.9521801,5,fp64,3431.563264
++regression_stats,10,39000,390000,metal,0,0.0006961673498153687,0.0006541251204907894,0.0008656666614115238,0.0002501250710338354,560210127.7852694,5,fp32,576.421888
++regression_stats,10,390000,3900000,cpu,1,0.032662583980709314,0.030701291747391224,0.03406220907345414,0.0,119402678.0705213,5,fp64,3431.858176
++regression_stats,10,390000,3900000,cpu,18,0.006654791999608278,0.006012291181832552,0.007818708196282387,0.0,586043861.3602898,5,fp64,3431.46496
++regression_stats,10,390000,3900000,metal,0,0.004117042291909456,0.002989500295370817,0.004763709381222725,0.000529208336956799,947281986.3094499,5,fp32,2962.440192
++regression_stats,100,390,39000,cpu,1,0.00036137504503130913,0.00033475039526820183,0.00036225002259016037,0.0,107921121.10735561,5,fp64,2962.440192
++regression_stats,100,390,39000,cpu,18,0.00017625000327825546,9.350012987852097e-05,0.00018370803445577621,0.0,221276591.62892938,5,fp64,3359.932416
++regression_stats,100,390,39000,metal,0,0.0003363746218383312,0.00026350002735853195,0.0005579171702265739,0.00019220833200961351,115942159.33074829,5,fp32,3255.451648
++regression_stats,100,3900,390000,cpu,1,0.0029982919804751873,0.0029679168947041035,0.003063875250518322,0.0,130074056.34263493,5,fp64,3432.742912
++regression_stats,100,3900,390000,cpu,18,0.0004399162717163563,0.00042741699144244194,0.00046166684478521347,0.0,886532335.9792868,5,fp64,781.484032
++regression_stats,100,3900,390000,metal,0,0.0005946666933596134,0.0005814996547996998,0.0005976245738565922,0.00023925001733005047,655829566.9741753,5,fp32,2962.440192
++regression_stats,100,39000,3900000,cpu,1,0.03219050029292703,0.03135691722854972,0.03299033408984542,0.0,121153755.44060485,5,fp64,3355.901952
++regression_stats,100,39000,3900000,cpu,18,0.0031737093813717365,0.003017541952431202,0.0036639999598264694,0.0,1228845975.2777827,5,fp64,3355.901952
++regression_stats,100,39000,3900000,metal,0,0.0044694580137729645,0.0031338329426944256,0.004542499780654907,0.0016885417280718684,872589022.6470106,5,fp32,3431.46496
++regression_stats,100,390000,39000000,cpu,1,0.3013692502863705,0.2989709582179785,0.3020119168795645,0.0,129409354.01651289,5,fp64,3431.87456
++regression_stats,100,390000,39000000,cpu,18,0.033760249614715576,0.0324889593757689,0.03822179138660431,0.0,1155204728.7885127,5,fp64,3359.932416
++regression_stats,100,390000,39000000,metal,0,0.03070899983868003,0.027952750213444233,0.031758958008140326,0.005229625036008656,1269986004.2617507,5,fp32,2913.845248
++regression_stats,1000,390,390000,cpu,1,0.0031211250461637974,0.0030487077310681343,0.0040359580889344215,0.0,124954942.28254408,5,fp64,3432.742912
++regression_stats,1000,390,390000,cpu,18,0.0006971252150833607,0.0005761669017374516,0.0007857088930904865,0.0,559440386.8369108,5,fp64,2962.440192
++regression_stats,1000,390,390000,metal,0,0.0005814996547996998,0.0005787923000752926,0.0009665000252425671,0.00020362494979053736,670679675.870723,5,fp32,3431.858176
++regression_stats,1000,3900,3900000,cpu,1,0.03439616598188877,0.033030624967068434,0.03468058304861188,0.0,113384730.20666131,5,fp64,781.484032
++regression_stats,1000,3900,3900000,cpu,18,0.003421790897846222,0.0031987917609512806,0.003632874693721533,0.0,1139754040.0422413,5,fp64,3431.514112
++regression_stats,1000,3900,3900000,metal,0,0.003796167206019163,0.0033167502842843533,0.004350459203124046,0.000579125015065074,1027352007.5238521,5,fp32,781.1072
++regression_stats,1000,39000,39000000,cpu,1,0.3240363751538098,0.3117389581166208,0.326583041343838,0.0,120356858.02709013,5,fp64,3431.46496
++regression_stats,1000,39000,39000000,cpu,18,0.031240916810929775,0.029546833131462336,0.03264595801010728,0.0,1248362851.7059293,5,fp64,3431.87456
++regression_stats,1000,39000,39000000,metal,0,0.026743208058178425,0.025766875129193068,0.02711204206570983,0.004475083318538964,1458314197.5771036,5,fp32,3360.11264
++regression_stats,10000,390,3900000,cpu,1,0.030644499696791172,0.030419666320085526,0.030872833915054798,0.0,127265905.41820379,5,fp64,3431.87456
++regression_stats,10000,390,3900000,cpu,18,0.003959249705076218,0.0036838343366980553,0.00489212479442358,0.0,985035117.8910861,5,fp64,2962.440192
++regression_stats,10000,390,3900000,metal,0,0.004190749954432249,0.00392800010740757,0.005979666020721197,0.0011161250295117497,930621020.6779948,5,fp32,3432.742912
++regression_stats,10000,3900,39000000,cpu,1,0.3569141672924161,0.3479222496971488,0.35834929207339883,0.0,109269969.01203898,5,fp64,2962.440192
++regression_stats,10000,3900,39000000,cpu,18,0.03749012481421232,0.03214179212227464,0.03947866568341851,0.0,1040273943.9591113,5,fp64,2962.440192
++regression_stats,10000,3900,39000000,metal,0,0.026574499905109406,0.026411292143166065,0.026990290731191635,0.004499250091612339,1467572301.9909616,5,fp32,3221.83168
++rolling_sumsq,1,390,390,cpu,1,9.578652679920197e-07,8.330680429935455e-07,1.0831281542778015e-06,0.0,407155382.94603795,5,fp64,3431.497728
++rolling_sumsq,1,390,390,cpu,18,7.920898497104645e-07,7.920898497104645e-07,8.749775588512421e-07,0.0,492368384.9029982,5,fp64,3431.87456
++rolling_sumsq,1,390,390,metal,0,0.0002839169465005398,0.0001594587229192257,0.0008917916566133499,1.8750084564089775e-05,1373641.146845944,5,fp32,3253.567488
++rolling_sumsq,1,3900,3900,cpu,1,7.4999406933784485e-06,7.33276829123497e-06,7.542315870523453e-06,0.0,520004111.9582764,5,fp64,3431.530496
++rolling_sumsq,1,3900,3900,cpu,18,7.4999406933784485e-06,7.415656000375748e-06,8.250121027231216e-06,0.0,520004111.9582764,5,fp64,3255.468032
++rolling_sumsq,1,3900,3900,metal,0,0.0002416251227259636,0.0001499168574810028,0.0002560419961810112,4.958361387252808e-06,16140705.718018986,5,fp32,2962.440192
++rolling_sumsq,1,39000,39000,cpu,1,6.93327747285366e-05,6.899982690811157e-05,7.020775228738785e-05,0.0,562504531.9864868,5,fp64,3355.8528
++rolling_sumsq,1,39000,39000,cpu,18,7.025012746453285e-05,6.979191675782204e-05,8.300039917230606e-05,0.0,555159135.0448426,5,fp64,781.1072
++rolling_sumsq,1,39000,39000,metal,0,0.00016458332538604736,0.00015858327969908714,0.00017341692000627518,1.9583385437726974e-05,236962036.75871435,5,fp32,2962.440192
++rolling_sumsq,1,390000,390000,cpu,1,0.0006914162077009678,0.000687750056385994,0.0007007499225437641,0.0,564059672.9671572,5,fp64,3432.742912
++rolling_sumsq,1,390000,390000,cpu,18,0.000718916766345501,0.0007105418480932713,0.0012256246991455555,0.0,542482827.2993312,5,fp64,2962.440192
++rolling_sumsq,1,390000,390000,metal,0,0.0007903752848505974,0.000574291218072176,0.0009351670742034912,6.225006654858589e-05,493436481.97921664,5,fp32,2962.440192
++rolling_sumsq,10,390,3900,cpu,1,7.1660615503787994e-06,7.000286132097244e-06,7.166992872953415e-06,0.0,544231998.6483852,5,fp64,3432.742912
++rolling_sumsq,10,390,3900,cpu,18,1.800013706088066e-05,1.5374738723039627e-05,2.3958273231983185e-05,0.0,216665016.87233216,5,fp64,3432.742912
++rolling_sumsq,10,390,3900,metal,0,0.0002032076008617878,0.00014958297833800316,0.0006746253930032253,1.4499993994832039e-05,19192195.486095995,5,fp32,17.170432
++rolling_sumsq,10,3900,39000,cpu,1,6.929086521267891e-05,6.908271461725235e-05,6.937514990568161e-05,0.0,562844754.2153615,5,fp64,2962.440192
++rolling_sumsq,10,3900,39000,cpu,18,4.487484693527222e-05,3.987457603216171e-05,5.0374772399663925e-05,0.0,869083744.313465,5,fp64,2962.440192
++rolling_sumsq,10,3900,39000,metal,0,0.00016070762649178505,0.00014404207468032837,0.00017450004816055298,1.9625062122941017e-05,242676722.01601195,5,fp32,2962.440192
++rolling_sumsq,10,39000,390000,cpu,1,0.0007095411419868469,0.0007064170204102993,0.000905290711671114,0.0,549651002.4886332,5,fp64,3432.742912
++rolling_sumsq,10,39000,390000,cpu,18,0.000132707878947258,0.00013195769861340523,0.00013837497681379318,0.0,2938785572.4451556,5,fp64,3358.88384
++rolling_sumsq,10,39000,390000,metal,0,0.0007357923313975334,0.0007097921334207058,0.0007738331332802773,9.062490426003933e-05,530040859.8432253,5,fp32,3431.46496
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++rolling_sumsq,10,390000,3900000,metal,0,0.002544207964092493,0.0024965000338852406,0.0026084999553859234,0.00076149997767061,1532893558.6407974,5,fp32,3253.567488
++rolling_sumsq,100,390,39000,cpu,1,6.991717964410782e-05,6.962474435567856e-05,7.033301517367363e-05,0.0,557802820.4014759,5,fp64,3368.943616
++rolling_sumsq,100,390,39000,cpu,18,0.00017983326688408852,0.00014462508261203766,0.0002232920378446579,0.0,216867550.01307648,5,fp64,2962.440192
++rolling_sumsq,100,390,39000,metal,0,0.0002676667645573616,0.00017749983817338943,0.0007679169066250324,9.541632607579231e-06,145703558.1705259,5,fp32,2962.440192
++rolling_sumsq,100,3900,390000,cpu,1,0.000806666910648346,0.0007096659392118454,0.0011533750221133232,0.0,483470928.151179,5,fp64,2962.440192
++rolling_sumsq,100,3900,390000,cpu,18,0.00020312517881393433,0.00012504169717431068,0.0002259998582303524,0.0,1919998309.797161,5,fp64,781.484032
++rolling_sumsq,100,3900,390000,metal,0,0.0006820829585194588,0.0003593750298023224,0.0008333330042660236,9.058334399014711e-05,571777956.2277012,5,fp32,3431.530496
++rolling_sumsq,100,39000,3900000,cpu,1,0.007338124793022871,0.007089000195264816,0.008123625069856644,0.0,531470928.88201374,5,fp64,2962.440192
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++rolling_sumsq,100,39000,3900000,metal,0,0.002226833254098892,0.0021508331410586834,0.002632542047649622,0.00043350004125386477,1751365978.0413911,5,fp32,3431.87456
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++rolling_sumsq,100,390000,39000000,metal,0,0.014852333813905716,0.014340042136609554,0.01528970804065466,0.0023322500055655837,2625849949.823083,5,fp32,3255.451648
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++rolling_sumsq,1000,390,390000,metal,0,0.0009075421839952469,0.000882917083799839,0.000995416659861803,2.3708329536020756e-05,429732090.5603684,5,fp32,2962.440192
++rolling_sumsq,1000,3900,3900000,cpu,1,0.00695441709831357,0.006937959231436253,0.006972583010792732,0.0,560794664.0050883,5,fp64,3432.742912
++rolling_sumsq,1000,3900,3900000,cpu,18,0.0010273326188325882,0.0008542081341147423,0.0010719997808337212,0.0,3796238850.5017724,5,fp64,556.466176
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++rolling_sumsq,10000,390,3900000,cpu,1,0.007047916762530804,0.007002290803939104,0.007088833022862673,0.0,553355002.8192397,5,fp64,3431.858176
++rolling_sumsq,10000,390,3900000,cpu,18,0.00107216602191329,0.001034500077366829,0.0011164997704327106,0.0,3637496358.111046,5,fp64,2962.440192
++rolling_sumsq,10000,390,3900000,metal,0,0.0021627498790621758,0.002053916919976473,0.0022570830769836903,0.0002617916325107217,1803259839.5941842,5,fp32,3431.858176
++rolling_sumsq,10000,3900,39000000,cpu,1,0.06922604190185666,0.06907229218631983,0.06939475005492568,0.0,563371802.4105898,5,fp64,3360.096256
++rolling_sumsq,10000,3900,39000000,cpu,18,0.00654304213821888,0.006384790875017643,0.00675958301872015,0.0,5960530159.540807,5,fp64,3432.742912
++rolling_sumsq,10000,3900,39000000,metal,0,0.014753291849046946,0.01457533286884427,0.01564762508496642,0.0025377500569447875,2643477835.254739,5,fp32,2962.440192

added experiments/results/bench_primitives_summary.json +4880 −0

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++ },
++ "shader_library": [
++  {
++   "backend": "metal",
++   "compiled_now": false,
++   "kernel": "shader_library_load",
++   "note": "metallib:/Users/simon-pierreboucher/Desktop/UQO/Recherche/Recherche-UQO/finance/wp40_raid/build/macos-release/raid.metallib chunks=1 convert_s=0.000001",
++   "seconds": 0.000230708,
++   "t": 0.03212570771574974,
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++  }
++ ]
++}
+ \ No newline at end of file

added experiments/results/fig_bench_primitives_throughput.pdf +0 −0

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added experiments/results/fig_bench_primitives_throughput.png +0 −0

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added include/raid/estimators/har.hpp +59 −0

++// HAR family (registry keys har.*). Daily series RV_t (t = 1..T), trading-day lags, causal construction:
++//   HAR-RV   (Corsi 2009):  y_{t+h} = β0 + βd RV_t + βw RV^{(5)}_t + βm RV^{(22)}_t + ε,  RV^{(k)}_t = (1/k) Σ_{j=0}^{k−1} RV_{t−j}
++//   log-HAR:               same with log RV on both sides (forecast = exp(ŷ) × smearing optional, not applied by default)
++//   HAR-X:                 + user covariates X_t (already aligned at t)
++//   HARQ (Bollerslev–Patton–Quaedvlieg 2016): βd → (βd + βq √RQ_t): term βq · √RQ_t · RV_t added
++//   Target for horizon h: y_{t+h} = (1/h) Σ_{j=1}^{h} RV_{t+j} (average over the next h days, "overlapping" when h > 1)
++//   or the single-day RV_{t+h} (`target = single`). Overlapping targets induce MA(h−1) errors → HAC with ≥ h−1 lags.
++#pragma once
++#include <vector>
++#include <span>
++#include <string>
++#include <Eigen/Dense>
++#include "raid/core/types.hpp"
++#include "raid/core/estimate.hpp"
++#include "raid/core/plan.hpp"
++#include "raid/estimators/ols.hpp"
++#include "raid/backend/backend.hpp"
++
++namespace raid::est {
++
++enum class HarTarget { average, single };
++
++struct HarSpec {
++  std::vector<usize> lags{1, 5, 22};   // daily, weekly, monthly windows
++  int horizon{1};
++  HarTarget target{HarTarget::average};
++  bool log{false};                      // log-HAR
++  bool harq{false};                     // add √RQ_t · RV_t
++  stats::CovOptions cov{stats::CovType::hac_bartlett, -1, false, {}, true};  // hac_lags −1 → max(h−1, ⌊4(n/100)^{2/9}⌋)
++  std::string model_key() const { return std::string(log ? "har.logrv" : "har.rv") + (harq ? ".harq" : "") + ".h" + std::to_string(horizon); }
++};
++
++/// Builds the aligned design (y, X) from a daily RV series (and optional RQ and exogenous columns X_t, aligned at t).
++struct HarDesign { Eigen::MatrixXd X; Eigen::VectorXd y; std::vector<std::string> names; usize first_t{0}; usize n{0}; };
++HarDesign har_design(std::span<const f64> rv, const HarSpec& spec, std::span<const f64> rq = {}, const Eigen::MatrixXd& exog = Eigen::MatrixXd(), const std::vector<std::string>& exog_names = {});
++
++/// Fit one HAR on one series (CPU QR + robust covariance). Estimate.extra contains fitted/residual summaries.
++Estimate har_fit(std::span<const f64> rv, const HarSpec& spec, std::span<const f64> rq = {}, const Eigen::MatrixXd& exog = Eigen::MatrixXd(), const std::vector<std::string>& exog_names = {});
++
++/// Forecast ŷ for the last available t (origin = last observation) from a fitted HAR; for log models returns exp(ŷ)
++/// (naive back-transform; the smearing factor is reported in extra["smearing"] and not applied).
++f64 har_forecast(const Estimate& fit, std::span<const f64> rv, const HarSpec& spec, std::span<const f64> rq = {}, const Eigen::VectorXd& exog_last = Eigen::VectorXd());
++
++/// Rolling (or expanding when window = 0) re-estimation with one-origin-ahead forecasts, strictly causal:
++/// the model fitted on observations ≤ t predicts y_{t+h}. Returns forecasts aligned with the target index.
++struct HarRolling { std::vector<usize> origin; std::vector<f64> forecast, actual; Eigen::MatrixXd coefficients; usize n_fits{0}; f64 seconds{0}; };
++HarRolling har_rolling(std::span<const f64> rv, const HarSpec& spec, usize window, usize step = 1, std::span<const f64> rq = {});
++
++/// Batched HAR over a panel of daily RV series (CSR). Sufficient statistics are accumulated by the backend (Metal when
++/// available: regression_stats) and solved in FP64 on the CPU; inference is classical (HAC requires residuals: use
++/// har_fit per series when robust SE are needed). Returns one Estimate per series.
++struct HarBatchResult { std::vector<Estimate> fits; backend::KernelStats stats; };
++HarBatchResult har_batch(std::span<const f64> rv_concat, std::span<const i64> offsets, const HarSpec& spec, const ExecutionPlan& plan = {});
++
++/// Forecast losses for volatility: MSE and QLIKE (Patton 2011): QLIKE = y/ŷ − log(y/ŷ) − 1.
++struct ForecastLoss { f64 mse, qlike; usize n; };
++ForecastLoss forecast_loss(std::span<const f64> actual, std::span<const f64> forecast);
++
++}  // namespace raid::est

added src/estimators/har.cpp +94 −0

++#include "raid/estimators/har.hpp"
++#include "raid/core/error.hpp"
++#include "raid/statistics/covariance.hpp"
++#include <chrono>
++#include <cmath>
++#include <algorithm>
++
++namespace raid::est {
++
++HarDesign har_design(std::span<const f64> rv, const HarSpec& spec, std::span<const f64> rq, const Eigen::MatrixXd& exog, const std::vector<std::string>& exog_names) {
++  const usize T = rv.size(); RAID_REQUIRE(!spec.lags.empty() && spec.horizon >= 1, invalid_argument, "har: lags and horizon");
++  const usize maxlag = *std::max_element(spec.lags.begin(), spec.lags.end()); const usize h = static_cast<usize>(spec.horizon);
++  RAID_REQUIRE(T > maxlag + h + 2, insufficient_samples, "har: need T > maxlag + h + 2");
++  for (f64 v : rv) RAID_REQUIRE(std::isfinite(v) && (!spec.log || v > 0), data_quality, "har: RV must be finite (and > 0 for log-HAR)");
++  if (spec.harq) RAID_REQUIRE(rq.size() == T, invalid_argument, "harq: RQ series required with the same length");
++  const usize nex = exog.size() ? static_cast<usize>(exog.cols()) : 0; if (nex) RAID_REQUIRE(static_cast<usize>(exog.rows()) == T, invalid_argument, "har-x: exog rows must equal T");
++  std::vector<f64> z(T); for (usize t = 0; t < T; ++t) z[t] = spec.log ? std::log(rv[t]) : rv[t];
++  // prefix sums for the window means (FP64, Neumaier)
++  std::vector<f64> cs(T + 1, 0.0); { f64 s = 0, c = 0; for (usize t = 0; t < T; ++t) { const f64 v = z[t], tt = s + v; if (std::abs(s) >= std::abs(v)) c += (s - tt) + v; else c += (v - tt) + s; s = tt; cs[t + 1] = s + c; } }
++  auto wmean = [&](usize t, usize k) { f64 s = 0; for (usize j = 0; j < k; ++j) s += z[t - j]; return s / static_cast<f64>(k); };  // direct sum (exact enough, k ≤ 22)
++  const usize first = maxlag - 1, last = T - 1 - h;  // origins t with full lags and a full target
++  HarDesign d; d.first_t = first; d.n = last - first + 1; const usize k = 1 + spec.lags.size() + (spec.harq ? 1 : 0) + nex;
++  d.X.resize(static_cast<Eigen::Index>(d.n), static_cast<Eigen::Index>(k)); d.y.resize(static_cast<Eigen::Index>(d.n));
++  d.names.push_back("const"); for (usize l : spec.lags) d.names.push_back((spec.log ? "logrv_" : "rv_") + std::to_string(l)); if (spec.harq) d.names.push_back("sqrt_rq_x_rv"); for (usize j = 0; j < nex; ++j) d.names.push_back(j < exog_names.size() ? exog_names[j] : "x" + std::to_string(j));
++  for (usize t = first; t <= last; ++t) {
++    const Eigen::Index i = static_cast<Eigen::Index>(t - first); Eigen::Index c = 0; d.X(i, c++) = 1.0;
++    for (usize l : spec.lags) d.X(i, c++) = wmean(t, l);
++    if (spec.harq) d.X(i, c++) = std::sqrt(std::max(rq[t], 0.0)) * rv[t];
++    for (usize j = 0; j < nex; ++j) d.X(i, c++) = exog(static_cast<Eigen::Index>(t), static_cast<Eigen::Index>(j));
++    if (spec.target == HarTarget::single) d.y[i] = z[t + h]; else { f64 s = 0; for (usize j = 1; j <= h; ++j) s += spec.log ? rv[t + j] : z[t + j]; s /= static_cast<f64>(h); d.y[i] = spec.log ? std::log(s) : s; }
++  }
++  return d;
++}
++
++Estimate har_fit(std::span<const f64> rv, const HarSpec& spec, std::span<const f64> rq, const Eigen::MatrixXd& exog, const std::vector<std::string>& exog_names) {
++  auto d = har_design(rv, spec, rq, exog, exog_names);
++  OlsOptions o; o.cov = spec.cov; o.names = d.names;
++  if (o.cov.type == stats::CovType::hac_bartlett && o.cov.hac_lags < 0) o.cov.hac_lags = std::max(spec.horizon - 1, stats::default_hac_lags(d.n));
++  auto r = ols(d.X, d.y, o); Estimate e = r.estimate; e.model = spec.model_key();
++  e.extra["horizon"] = spec.horizon; e.extra["target"] = spec.target == HarTarget::average ? "average" : "single"; e.extra["lags"] = spec.lags; e.extra["first_origin"] = d.first_t; e.extra["log"] = spec.log; e.extra["harq"] = spec.harq;
++  if (spec.log) { f64 s = 0; for (Eigen::Index i = 0; i < r.residuals.size(); ++i) s += std::exp(r.residuals[i]); e.extra["smearing"] = s / static_cast<f64>(r.residuals.size()); }
++  return e;
++}
++
++f64 har_forecast(const Estimate& fit, std::span<const f64> rv, const HarSpec& spec, std::span<const f64> rq, const Eigen::VectorXd& exog_last) {
++  const usize T = rv.size(); const usize maxlag = *std::max_element(spec.lags.begin(), spec.lags.end()); RAID_REQUIRE(T >= maxlag, insufficient_samples, "har_forecast: not enough history");
++  const usize t = T - 1; f64 yhat = fit.coefficients[0]; usize c = 1;
++  for (usize l : spec.lags) { f64 s = 0; for (usize j = 0; j < l; ++j) s += spec.log ? std::log(rv[t - j]) : rv[t - j]; yhat += fit.coefficients[c++] * s / static_cast<f64>(l); }
++  if (spec.harq) { RAID_REQUIRE(rq.size() == T, invalid_argument, "harq forecast needs RQ"); yhat += fit.coefficients[c++] * std::sqrt(std::max(rq[t], 0.0)) * rv[t]; }
++  for (Eigen::Index j = 0; j < exog_last.size(); ++j) yhat += fit.coefficients[c++] * exog_last[j];
++  return spec.log ? std::exp(yhat) : yhat;
++}
++
++HarRolling har_rolling(std::span<const f64> rv, const HarSpec& spec, usize window, usize step, std::span<const f64> rq) {
++  const auto t0 = std::chrono::steady_clock::now(); HarRolling out; const usize T = rv.size(); const usize h = static_cast<usize>(spec.horizon);
++  const usize maxlag = *std::max_element(spec.lags.begin(), spec.lags.end()); const usize minT = maxlag + h + 30;
++  RAID_REQUIRE(window == 0 || window >= minT, insufficient_samples, "har_rolling: window too small"); RAID_REQUIRE(T > minT + h, insufficient_samples, "har_rolling: series too short");
++  const usize k = 1 + spec.lags.size() + (spec.harq ? 1 : 0); std::vector<Eigen::VectorXd> coefs;
++  for (usize end = (window ? window : minT); end + h <= T; end += step) {       // model uses rv[0..end) (or the last `window`), forecasts target at origin end−1
++    const usize b = window ? end - window : 0; std::span<const f64> hist = rv.subspan(b, end - b); std::span<const f64> rqh = spec.harq ? rq.subspan(b, end - b) : std::span<const f64>();
++    Estimate e; try { HarSpec s2 = spec; s2.cov.type = stats::CovType::classical; e = har_fit(hist, s2, rqh); } catch (const RaidError&) { continue; }
++    const f64 fc = har_forecast(e, hist, spec, rqh); const usize t = end - 1;
++    f64 actual; if (spec.target == HarTarget::single) actual = rv[t + h]; else { f64 s = 0; for (usize j = 1; j <= h; ++j) s += rv[t + j]; actual = s / static_cast<f64>(h); }
++    out.origin.push_back(t); out.forecast.push_back(fc); out.actual.push_back(actual); coefs.push_back(Eigen::Map<const Eigen::VectorXd>(e.coefficients.data(), static_cast<Eigen::Index>(k))); ++out.n_fits;
++  }
++  out.coefficients.resize(static_cast<Eigen::Index>(k), static_cast<Eigen::Index>(coefs.size())); for (usize j = 0; j < coefs.size(); ++j) out.coefficients.col(static_cast<Eigen::Index>(j)) = coefs[j];
++  out.seconds = std::chrono::duration<f64>(std::chrono::steady_clock::now() - t0).count(); return out;
++}
++
++HarBatchResult har_batch(std::span<const f64> rv_concat, std::span<const i64> offsets, const HarSpec& spec, const ExecutionPlan& plan) {
++  HarBatchResult out; const usize S = offsets.size() - 1; std::string why; auto be = backend::resolve(plan, &why);
++  // Build all designs (CPU, FP64), concatenate row-major for the backend, accumulate X'X / X'y / y'y per series, solve in FP64.
++  std::vector<HarDesign> designs(S); usize k = 0, rows = 0; std::vector<i64> roff(S + 1, 0); std::vector<usize> ok(S, 1);
++  for (usize s = 0; s < S; ++s) { try { designs[s] = har_design(rv_concat.subspan(static_cast<usize>(offsets[s]), static_cast<usize>(offsets[s + 1] - offsets[s])), spec); k = static_cast<usize>(designs[s].X.cols()); rows += designs[s].n; } catch (const RaidError&) { ok[s] = 0; } roff[s + 1] = static_cast<i64>(rows); }
++  RAID_REQUIRE(k > 0, insufficient_samples, "har_batch: no series with enough data");
++  std::vector<f64> X(rows * k), y(rows); for (usize s = 0; s < S; ++s) { if (!ok[s]) continue; const usize b = static_cast<usize>(roff[s]); for (usize i = 0; i < designs[s].n; ++i) { y[b + i] = designs[s].y[static_cast<Eigen::Index>(i)]; for (usize j = 0; j < k; ++j) X[(b + i) * k + j] = designs[s].X(static_cast<Eigen::Index>(i), static_cast<Eigen::Index>(j)); } }
++  std::vector<f64> xtx, xty, yty; be->regression_stats(X, y, roff, k, xtx, xty, yty, &out.stats);
++  out.fits.resize(S);
++  for (usize s = 0; s < S; ++s) {
++    if (!ok[s]) { out.fits[s].model = spec.model_key(); out.fits[s].convergence = Convergence{false, 0, 0, 0, 1, "insufficient data"}; continue; }
++    SufficientStats ss; ss.xtx = Eigen::Map<const Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>>(xtx.data() + s * k * k, static_cast<Eigen::Index>(k), static_cast<Eigen::Index>(k)); ss.xty = Eigen::Map<const Eigen::VectorXd>(xty.data() + s * k, static_cast<Eigen::Index>(k)); ss.yty = yty[s]; ss.n = designs[s].n;
++    OlsOptions o; o.names = designs[s].names; auto r = ols_from_stats(ss, o); out.fits[s] = r.estimate; out.fits[s].model = spec.model_key(); out.fits[s].backend = be->kind(); out.fits[s].precision = out.stats.precision;
++    out.fits[s].extra["horizon"] = spec.horizon; out.fits[s].extra["note"] = "classical SE from sufficient statistics; use har_fit for HAC";
++  }
++  return out;
++}
++
++ForecastLoss forecast_loss(std::span<const f64> a, std::span<const f64> f) {
++  RAID_REQUIRE(a.size() == f.size(), invalid_argument, "forecast_loss: size mismatch"); ForecastLoss l{0, 0, 0};
++  for (usize i = 0; i < a.size(); ++i) { if (!(a[i] > 0) || !(f[i] > 0) || !std::isfinite(a[i]) || !std::isfinite(f[i])) continue; const f64 d = a[i] - f[i]; l.mse += d * d; const f64 q = a[i] / f[i]; l.qlike += q - std::log(q) - 1.0; ++l.n; }
++  if (l.n) { l.mse /= static_cast<f64>(l.n); l.qlike /= static_cast<f64>(l.n); } return l;
++}
++
++}  // namespace raid::est

spb/wp40_uqo

WP40 RAID: Phase 3 gate — primitives benchmark records, summary, figure; status/progress updated

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