Float moment — first and second statistical moments¶

float_moment computes the mean (first moment) and mean of squares (second moment) of the reference and distorted luma planes. It is a building block for higher-level statistical metrics and a sanity-check extractor when validating decoder output. Run it with --feature float_moment; features lists every extractor.

Run it¶

• CLI: --feature float_moment.
• ffmpeg: libvmaf=feature=name=float_moment.
• C API: vmaf_use_feature(ctx, "float_moment", NULL).

Output metrics:

• float_moment_ref1st, float_moment_dis1st — first moment (mean).
• float_moment_ref2nd, float_moment_dis2nd — second moment (mean of squares).

Output range — for 8-bit luma, [0, 255] for the first moment and [0, 65 025] for the second; scales with \(2^{\mathrm{bpc}} - 1\).

Input formats — YUV 4:2:0 / 4:2:2 / 4:4:4, 8 / 10 / 12 / 16 bpc. Y plane only.

Options — none.

Limitations — Stateless per frame. Float pipeline: the picture plane is copied to float32 before the moments are computed. A fixed-point twin is not shipped.

Backends¶

With --backend cuda, sycl, hip or metal, --feature float_moment runs that backend's twin, and the feature_backends list of the JSON output names it:

vmaf ... --backend cuda --feature float_moment   # runs float_moment_cuda

How the twins match the CPU¶

The GPU kernels accumulate four integer sums per frame in a single dispatch. The CPU squares each sample in fp32, which rounds above 12 bits. float_moment_cuda (ADR-1453), float_moment_hip (ADR-1447) and float_moment_sycl (ADR-1449) add that fp32 square as an integer.

On a 16-bit frame of more than 2 097 152 pixels the sum of squares can pass \(2^{53}\) units, and from there the CPU's own double rounds as it adds. Since ADR-1497 the twins form that rounded sum on the device and equal the CPU extractor at 8, 10, 12 and 16 bits on every frame.

How the CPU SIMD paths match the scalar path¶

The CPU kernels return the same bits whichever instruction set runs: the AVX2, AVX-512, NEON and SVE2 kernels square in vectors and add the values into one double one after the other, in the scalar loop's order. The second moment of a 16-bit 4K frame is therefore the same on x86 and aarch64 and on every SVE vector length. test_moment_simd has the cases.

History¶

• 2026-10-03 — ADR-1500: the NEON and SVE2 kernels used to add in lanes and could return a different last digit on 16-bit 4K frames; they now add in the scalar loop's order.
• 2026-10-01 — --backend <gpu> --feature float_moment computed the feature on the CPU and warned that the backend had no twin; the twin ran only when named (--feature float_moment_cuda). It now runs the twin.