fix(cuda): add the float_motion SAD in the CPU's order so the twin is bit-identical

[lusoris]

Summary

float_motion_cuda now returns the CPU float_motion scores bit for bit: motion, motion2 and motion3 are identical on every frame measured, with no measurable change in time.

Builds on #1695 (every CUDA fatbin without FMA contraction, landed as 691ca5677): the blur is the CPU's only with that flag.

Closes T-CUDA-FLOAT-MOTION-CPU-FLOAT-SUM-2026-10-01, which #1695 found. The CPU extractor adds the absolute differences of a row into one float, the row sums into a second float, and divides in float. Those running sums round at every step, so the score depends on the order of the additions. The twin summed each 16x16 block on the device and the blocks in double on the host, which is closer to the exact mean and up to 1.36e-4 from the CPU on 1920x1080 checkerboards, above the 5e-5 tolerance of ADR-0214. The gate runs the Netflix pair only (3.1e-6), so it passed.

What changed

• core/src/feature/cuda/float_motion/float_motion_score.cu: the two blur kernels write the blurred plane only. A new float_motion_row_sad kernel runs one thread per row and adds |cur[j] - prev[j]| left to right into one fp32 accumulator; the readback is one float per row.
• core/src/feature/float_motion_sad.h (new, backend neutral): the tail of compute_motion_simd(), one float over the rows and a float division. float_motion_cuda.c keeps no sum of its own.
• scripts/ci/cross_backend_calibration.py: EXACT_TWINS lists float_motion: cuda, so the parity gate compares that cell with tolerance 0 at --precision max.
• ADR-1409 records the contract. The SYCL, HIP and Metal twins still sum per block (T-GPU-FLOAT-MOTION-CPU-FLOAT-SUM-2026-10-01, opened here).

Type

• feat — new feature
• fix — bug fix
• perf — performance improvement
• refactor — no behavior change
• docs — documentation only
• test — test-only
• build / ci — tooling / infra
• port — cherry-pick from upstream Netflix/vmaf
• sycl / cuda / simd — backend-specific

Checklist

• Commits follow Conventional Commits (the commit-msg hook enforces this).
• make format && make lint is green locally. (clang-format and clang-tidy on the touched files: 0 warnings in them; the commit hooks.)
• Unit tests pass: python3 scripts/ci/run_meson_test.py -- -C build. (--suite=fast on a CUDA build, RTX 4090: 264 of 264 on the current tip.)
• If I touched any SIMD/GPU code path, I ran /cross-backend-diff and the worst ULP is ≤ 2. (0; table below.)
• If I touched a feature extractor with SIMD/GPU twins, I either updated every twin or listed the gap under "Known follow-ups" below. (SYCL, HIP and Metal are listed there.)
• If I added a new .c / .cpp / .cu / .h / .hpp, it has the appropriate license header (see CONTRIBUTING.md).
• If this is a breaking change, the commit message uses ! or BREAKING CHANGE: and the migration path is documented below. (Not a breaking change.)
• If this PR adds an ADR, the ADR row lives in docs/adr/_index_fragments/<NNNN-slug>.md.

Bug-status hygiene (ADR-0165)

• docs/state.md updated in this PR: T-CUDA-FLOAT-MOTION-CPU-FLOAT-SUM-2026-10-01 moved to Recently closed with the evidence; T-GPU-FLOAT-MOTION-CPU-FLOAT-SUM-2026-10-01 opened for the other three twins.

Netflix golden-data gate (ADR-0024)

• I did not modify any assertAlmostEqual(...) score in the Netflix golden Python tests.
• If I believe a golden value must change, I have explained why below AND pinged @lusoris for a CODEOWNERS exception. (None changes: no CPU code is touched.)

Cross-backend numerical results

RTX 4090, nvcc 13.4, --precision max, float_motion on --backend cpu against float_motion_cuda. Frames identical and largest absolute difference over motion, motion2 and motion3. "Before" is master 691ca5677 (#1695).

fixture                                   frames  before                    after
Netflix 576x324                           48      at most 1/48, 3.1e-6      48/48, 0
checkerboard 1 px, 1920x1080              3       at most 1/3,  1.36e-4     3/3,   0
checkerboard 10 px, 1920x1080             3       at most 1/3,  1.36e-4     3/3,   0
BBB 3840x2160                             200     at most 1/200, 2.4e-5     200/200, 0
gradient and noise 1920x1080              6       -                         6/6,   0
gradient and noise 1280x720, 10-bit       4       -                         4/4,   0
Netflix crop 573x163, 4:4:4               48      -                         48/48, 0
Netflix, motion_fps_weight=0.5 mmxv=3     48      -                         48/48, 0
Netflix, blend factor 0.5, offset 2       48      -                         48/48, 0

The one frame that matched before is frame 0, whose motion and motion2 are 0 by definition.

scripts/ci/cross_backend_parity_gate.py --features float_motion --backends cpu cuda reports tol=0.0e+00 (exact:ADR-1397) max_abs_diff=0.000e+00 OK on all four fixtures (BBB: all 200 frames).

Performance (if perf or feat)

Not a performance change; measured because the row kernel uses one thread per row. vmaf tool, BBB 3840x2160, 200 frames, 25 alternating before/after pairs, host load 12 to 14:

twin                 before   after   paired difference (median, quartiles)
float_motion_cuda    3.00     2.98    -0.12 ms  (-0.57 .. +0.25)
float_psnr_cuda      2.84     2.80    -0.03 ms  (-0.23 .. +0.49)   untouched control

Deep-dive deliverables (ADR-0108)

• Research digest — no digest needed: the cause was analysed in Research-1403 (the host replay of the checkerboard), and the measurements of the fix are in ADR-1409 and the docs/state.md row.
• Decision matrix — ADR-1409 ## Alternatives considered.
• AGENTS.md invariant note — core/src/feature/cuda/AGENTS.md (one thread per row, plain loop, host helper, no other reduction), scripts/ci/AGENTS.md (EXACT_TWINS), and docs/development/rebase-sensitive-invariants.md.
• Reproducer / smoke-test command — pasted below under "Reproducer".
• CHANGELOG fragment — changelog.d/fixed/cuda-float-motion-cpu-float-sum.md.
• Rebase note — docs/rebase-notes.md, ADR-1409.

Reproducer

meson setup build-cuda core -Denable_cuda=true -Denable_sycl=false --buildtype=release
ninja -C build-cuda
# Fail on master by 2.0e-5 and 6.2e-5; need a CUDA device.
build-cuda/test/test_cuda_float_motion_parity
build-cuda/test/test_cuda_float_motion_parity_large
# No device needed.
build-cuda/test/test_float_motion_sad
python3 -m pytest core/test/test_cuda_kernel_source_contract.py scripts/ci/test_cross_backend_parity_gate.py
# The gate cell, tolerance 0.
python3 scripts/ci/cross_backend_parity_gate.py --vmaf-binary build-cuda/tools/vmaf \
  --reference python/test/resource/yuv/checkerboard_1920_1080_10_3_0_0.yuv \
  --distorted python/test/resource/yuv/checkerboard_1920_1080_10_3_1_0.yuv \
  --width 1920 --height 1080 --features float_motion --backends cpu cuda

Known follow-ups

• float_motion_sycl, float_motion_hip, float_motion_metal still sum per block: T-GPU-FLOAT-MOTION-CPU-FLOAT-SUM-2026-10-01. The host helper is backend neutral; each twin needs the row kernel; the blur is already built without contraction on SYCL (ADR-1367) and HIP (fix(hip): compile every HIP kernel with contraction off through one shared flag list #1694).
• The gate's float_motion cell compares motion and motion2; motion3 is covered by test_cuda_float_motion_parity, because the SYCL twin does not emit it yet.