D120 - Controlled-ISA: pinning the fast SFU path against the correctly-rounded one, through the precision the SPIR-V asks for

Status: derived - three relaxed-precision variant kernels (rcprelaxed, sqrtrelaxed, divrelaxed), sharing the correctly-rounded reference with their full forms; the machinery is verified as plumbing on llvmpipe, and the finding it produces waits on RDNA hardware.

The census marks the reciprocal, sqrt and division as covered, but that hides a distinction the shader gap turns on. A full-precision 1.0/x is not one instruction on RDNA - it is the correctly-rounded IEEE division sequence (v_div_scale, v_rcp, v_div_fmas, v_div_fixup). The bare v_rcp, ~1 ULP off, is a different result, and a game's shaders reach it by asking for relaxed precision. Whether an emulator must reproduce the fast path bit-for-bit or can compute the correct value depends on which the title used - so obSCEne has to probe both, not just one.

The lever is the precision decoration, not hand-written SPIR-V. A mediump reciprocal compiles to a RelaxedPrecision-decorated division (confirmed: five such decorations in rcprelaxed against zero in full rcp), which RDNA lowers to the bare fast op; the full-precision kernel gets the correct sequence. This is exactly the lever a real shader pulls, so it is more faithful than forcing an opcode by hand and less fragile - the driver honours the hint rather than being tricked past an optimiser. spirv-as is available for the cases GLSL genuinely cannot express, but the fast/correct split is not one of them.

Two honest boundaries recorded in the census as it changed:

• The division primitives are a sequence, not isa. div_scale, div_fixup and div_fmas have no SPIR-V opcode and no GLSL - they exist only as the driver's decomposition of a full-precision division. They cannot be isolated, but they are not unreached: full divf/rcp exercise the whole sequence, and its end-to-end correctness against the reference is the check. A new reachability, sequence, says this rather than pretending the primitives are either covered or unreachable. fdiv_fast, by contrast, is the fast path and is now covered by divrelaxed.
• The reference is shared, deliberately. rcprelaxed references the same correctly-rounded 1/x as rcp. That is the point: on hardware the relaxed kernel diverges from it (the fast-path error) while the full kernel matches, so the diff against the reference reads directly as "this side is approximate, that side is exact". On llvmpipe, which ignores the hint, both match and agree bit-for-bit (rcp and rcprelaxed of 1/3 are both 0x3eaaaaab) - the plumbing proven, the finding deferred to the part that honours the decoration.