D148 - gpustats: the diff as a distance, so the approximation is a number, not a yes/no

Status: derived - obscene-tool gpustats device reference reports per-kernel ULP statistics, ranked worst first. Proven on the llvmpipe golden against its reference, and it surfaced a real finding on the first run.

gpudiff answers "does this lane match" - right for the exact operations and the regression gate. The transcendentals need the other question: they are allowed to be approximate, so what matters is by how much. gpustats reduces a corpus-against-reference diff to a ULP distance per kernel - lanes, exact, diverged, max and mean ULP, and the worst lane as an example - ranked so the worst approximation is on top. On llvmpipe today it names that rasteriser's error; on a Deck's corpus it is RDNA2's; against an emulator's corpus it is the shader gap, measured.

The first run found the shape of the problem: the well-behaved SFU ops sit at 1-6 ULP (rsq 1, exp2 2, exp and cosh 6), and the catastrophic divergence is large-argument trig - sin/tan/cos of ~1e20 return a value on the wrong side of the range reduction entirely. That is exactly the kind of thing the tool exists to rank.

Two choices the first output forced, each a small piece of numerical honesty:

• Signed zeros are zero ULP apart. The ordering maps +0 and -0 to the same point, because they compare equal as numbers and the sign of a zero is a bit fact gpudiff already catches, not an approximation error. The naive 0x80000000 - bits transform put them 2^32 apart and made min/max/pow/sinh look catastrophically wrong on their signed-zero lanes; the mirror-magnitude transform fixes it.
• Integer-output kernels are omitted, by name. ULP is a distance between floats; cvti, bitcount, bfe, the packs and the rest output an integer, a bitfield or a packed word, and reading those bits as a float gives a number nobody computed. They are gpudiff's domain (exact-or-bug), so gpustats skips them and says so. The list is by name because the record carries no type tag - a comment marks that a new integer-output kernel must be added to it.

Not a gate: it is an analysis tool, like gpuref, so it prints and exits 0. Its correctness is in the unit tests (the ULP of adjacent floats, of signed zeros, of a NaN against a number), which the tool suite runs; it needs no verify.sh step because it produces no committed artifact that could drift.