Research-2109: Integer ADM Barten fixed-point normalization — 2026-09-25¶
Status: Complete
Authority inspected: signed collector 9e1b8d435dd858169bcfa3750f480d6129730450
Scope: correctness of adm_csf_mode=1 on CPU and the CUDA, SYCL, HIP, and Metal integer-ADM twins. No benchmark, tuning, retraining, model weight, score snapshot, Netflix golden assertion, dependency, public API, or FFmpeg surface change.
Failure and hypothesis¶
On the canonical 576x324 Netflix pair, the original fixed-point mode 1 published NaN for integer_adm2, integer_aim, and scale 1 and collapsed the other scale scores toward zero. ADR-1191 replaced the silent narrowing with -EINVAL, but the documented default Barten configuration remained unusable.
The raw weights explain the failure. Watson97 is near 1e-2; Barten at the default scale is about 1.21 at DWT scale 0 and 26.98 at scale 3. Multiplying those values by the existing Q21/Q23/Q32 factors overflows the scale-0 uint16_t representation and consumes the signed headroom of later CSF and contrast-masking operations. Widening only the stored weight cannot work: the weighted bands and the cube accumulator remain bounded.
The checked hypothesis was that one power-of-two exponent per scale can retain the three bands' ratios, keep every downstream integer inside its existing budget, and be restored exactly after the contrast-masking cube.
Headroom experiment¶
The raw fixed-point values were divided by the smallest shared 2^k below a candidate scale-1..3 ceiling, then exercised through the real CPU extractor on a deterministic textured pair:
| Scale-1..3 exclusive ceiling | Result |
|---|---|
| 2^32 | scales 1 and 2 still published NaN |
| 2^31 | scale 1 still published NaN |
| 2^30 | all seven mode-1 outputs finite and non-degenerate |
Scale 0 remains storage-limited to values below 2^16. The 2^30 ceiling leaves two headroom bits for the signed CSF/CM arithmetic and cube accumulation.
For each scale, all three bands use the same exponent k; choosing separate exponents would change the metric. Because contrast masking accumulates the cube of the normalized signal, its final power-of-two divisor subtracts 3k. The denominator continues to multiply by the original floating-point CSF factors. With k=0, conversion and CPU SIMD dispatch are unchanged.
Float-reference comparison¶
The exact collector's 576x324 Netflix pair was scored once with fixed-point adm=adm_csf_mode=1 and once with float_adm=adm_csf_mode=1. Pooled means:
| Output | Integer ADM | Float ADM | Absolute delta |
|---|---|---|---|
adm2 | 0.939569 | 0.939583 | 0.000014 |
aim | 0.017911 | 0.017910 | 0.000001 |
adm3 | 0.960829 | 0.960836 | 0.000007 |
| scale 0 | 0.763542 | 0.763569 | 0.000027 |
| scale 1 | 0.848033 | 0.848042 | 0.000009 |
| scale 2 | 0.916561 | 0.916575 | 0.000014 |
| scale 3 | 0.961231 | 0.961247 | 0.000016 |
The maximum pooled absolute difference is 2.7e-5, inside the places=4 cross-backend contract and far from the prior NaN/near-zero failure.
Backend coupling¶
adm_csf_fixed_point.h owns the limits and conversion. CPU, CUDA, SYCL, HIP, and Metal store k for each scale and restore 3k in their host-side CM finalizers. CUDA and Metal apply it to DLM and AIM. SYCL and HIP do not provide AIM/ADM3, so they apply it to ADM2 and per-scale outputs only. Every denominator uses the unnormalized float factors.
Metal integer ADM previously rejected every nonzero CSF mode despite declaring the CPU range. It now uses the common factor selection and normalization for modes 0–3, and its adm_csf_mode entry no longer carries VMAF_OPT_FLAG_DEFAULT_ONLY. GPU float_adm remains mode-0-only.
Verification¶
test_adm_csf_representablepasses all six cases, including finite, non-degenerate mode-1adm2,aim, andadm3, an already-representable Barten configuration, the maximum accepted Barten scale, and continued rejection of an invalid blend-table geometry.- The canonical CPU run above completed in an isolated, device-less container; no live
vmaf-dev-mcpcontainer was touched. - CUDA and HIP wrappers plus their mode-1 parity executables compile and link in isolated no-device builds. On the idle local AMD
gfx1036, the real HIP kernel build passes all five focused cases, including mode-1 parity at places=4. The CUDA executable returns Meson's hardware skip status 77 when no device is passed through; the local RTX 4090 was already occupied, so it was deliberately not multiplexed. - The SYCL kernel and mode-1 parity executable compile and link under oneAPI 2026.1. Its inherited LTO/plugin mismatch was isolated by setting
b_lto=falsefor this verifier; the device-less run then skips with status 77 as designed. - The device-free option-capability contract passes with Metal integer ADM removed from the default-only inventory. The Metal parity source includes a places=4 mode-1 case; an Apple hardware run remains the platform gate.
Result¶
Full-scale Barten is a valid fixed-point ADM configuration again. It produces finite, reference-consistent scores without weakening invalid-input guards or changing already-representable arithmetic. Performance work is intentionally deferred until the correctness-first RC1 cleanup is complete.