ADR-1450: float_psnr_sycl adds its squared differences as integers, and is bit-identical to the CPU¶

• Status: Accepted
• Date: 2026-10-02
• Deciders: lusoris
• Tags: sycl, gpu-parity, numerics, psnr, testing, ci, rc3, fork-local

Context¶

float_psnr.c converts both luma planes to float (dividing a sample by scaler = 2^(bpc - 8)), squares each difference in float and adds the squares in double, row by row. Every term is a float and a multiple of 1 / scaler^2, and the sum does not round while it is below 2^53 of those units, so the CPU's noise is the exact sum of its terms.

float_psnr_sycl formed the same terms and added them in fp32: per sub-group and per 16x16 work-group, with the work-groups added in double on the host. A group of 256 terms is exact in fp32 only while its sum needs at most 24 bits in the unit of the smallest term. At 8 bits that always holds (256 squares below 2^16). At 10, 12 and 16 bits it holds while the group's rms difference stays below 256 code values, which natural content at moderate distortion does. ADR-1440 found and fixed this in the HIP twin and named the SYCL twin from its source.

A sweep of every SYCL twin on high-bit-depth and full-range fixtures (ADR-1449) measured it on an Arc A380 (xe driver) at --precision max against --backend cpu of the same build (T-SYCL-FLOAT-PSNR-FP32-BLOCK-SUMS-2026-10-02):

The repository's high-bit-depth Netflix fixtures are the 8-bit clip shifted left, which is why the earlier survey on the gate's fixtures saw nothing.

Decision¶

We will add the squares as integers. The kernel squares the raw sample difference in float, which is the CPU's term times scaler^2 (the same significand: the CPU's samples are the raw ones divided by a power of two, so up to 12 bits the square is exact and at 16 bits both round it to 24 bits), and converts the product, an integer below 2^32, to uint64. The sub-group reduction, the work-group total and the read-back are uint64. The host adds the work-groups in uint64, converts the total to double and divides by scaler^2 and by the pixel count. The device's sum is exact at every bit depth, and the conversion is exact below 2^53, so the twin's noise is the CPU's wherever the CPU's own sum is exact. float_psnr: sycl is declared an exact twin.

fpsnr_pixel_noise() and fpsnr_store_workgroup_sum() are always inlined: a call left in a kernel takes scratch memory (ADR-1395).

Alternatives considered¶

Consequences¶

• Positive: measured on an Arc A380 at --precision max, the score of every frame equals --backend cpu of the same build: 288 of 288 on the fixtures above (269 before); the same with uncapped=true.
• Negative: 3 % more time at 3840x2160. Medians of 7 runs of the vmaf tool, twin alone, host load average 13: 3.31 ms before and 3.41 ms after per 3840x2160 frame, 0.12 and 0.12 ms per 576x324 frame (a psnr_sycl control read 2.93 and 2.94 ms).
• Negative: at 16 bits the equality has a bound that comes from the CPU, not from the twin. The CPU's running sum is exact below 2^53 units of 2^-16, a mean squared error of 2^37 / (width * height) on the 8-bit scale: 16570 at 3840x2160 (a PSNR below 6 dB), 66000 at 1920x1080 (above the largest possible error). Beyond it the CPU rounds each further add of a row's sum, and the twin, which rounds the exact sum once, is within 10 / ln(10) * (rows + 1) * 2^-53 dB of it plus a few units in the last place (7e-13 dB at 1440 rows). test_sycl_float_psnr_parity asserts that bound on a 2560x1440 frame past 2^53; the two scores were equal there.
• Negative: stored float_psnr_sycl scores of high-bit-depth input with large differences change by up to 7.4e-8 dB.
• Neutral / follow-ups:
• Against a GCC build of the CPU extractor 6 of 288 frames differ by at most 1.4e-14 dB. The noise is equal there; the score is 10 * log10(...) on the host, and an icx build links Intel's log10 where a GCC build links glibc's. The CPU extractor of an icx build differs from a GCC build on the same frames (T-ICX-LIBIMF-HOST-MATH-2026-10-01).
• float_psnr_cuda and float_psnr_metal reduce in fp32 the same way by their sources; other lanes own them.
• Guards: test_sycl_float_psnr_parity and its _large variant (== on two frames of full-range noise at 8, 10, 12 and 16 bits, with uncapped, on a bright 16-bit 1920x1080 pair and on identical frames; the bound past 2^53; six of the nine score cases fail on the fp32 twin) and test_sycl_float_psnr_exact_contract.py (nine planted regressions, no device). The cases live in core/test/float_psnr_twin_parity.h for another backend's test to instantiate.

References¶

• req (coordinator brief for the SYCL exactness lane, 2026-10-01): "User direction: results before speed; a twin reproduces the CPU bit for bit, tuning comes afterwards."
• req (same brief): "Then measure every other SYCL twin against the CPU at --precision max on the A380 (Netflix pair, both 1080p checkerboards, testdata/bbb 4K), list which are bit-identical and which are not with the max abs diff, and fix the non-identical ones one PR each in order of the largest difference, isolating the cause per term (types, rounding points, libm calls, reduction order)."
• ADR-1440, ADR-1449, ADR-1395, ADR-1193, ADR-1421, ADR-1428, ADR-0214.
• docs/state.md: T-SYCL-FLOAT-PSNR-FP32-BLOCK-SUMS-2026-10-02.