nx_vecmath_slerp_candidate_t181.nx

nx_vecmath.nx -- THE SHARED INTEGER LINEAR-ALGEBRA FOUNDATION (PG2, procgen.plan, 2026-08-24). WHY THIS EXISTS, MEASURED NOT ASSERTED: before this file the estate's entire shared math foundation was nx_itrig.nx at 1151 bytes -- it_sin4096 and it_cos4096 and nothing else. Every consumer above it re-rolled its own primitives: nx_gsplat carries gs_isqrt AND a private exp-LUT, nx_bodybench carries a private acos LUT. Three duplicate rulers for two operations. Worse, with no quaternion type nx_gsplat's gs_set_aniso had to settle for a normal-plus-tangent SURFEL where full 3D gaussian covariance needs quaternion-plus-3-axis scale -- a capability ceiling caused by a missing primitive, not by a design choice. SCALE IS DERIVED, NOT PICKED: VM_ONE = 4096 because that is already the estate's unit. nx_itrig emits fx4096 and measures angles in rad*4096; nx_vmd decodes quaternions at V_SCALE_ROT = 4096. Adopting any other scale would have made this file a converter instead of a foundation. Every other constant here is either derived from VM_ONE arithmetically or carries its derivation on its own line. COMPOSES THE INCUMBENT: sine and cosine come from nx_itrig by import. This file does NOT re-derive Taylor coefficients. VM_PI and VM_PI2 restate nx_itrig's angle constants because NishiLang const scope does not cross the import, so nx_vecmath_gate carries a tooth that FAILS if the two ever disagree -- a guarded duplicate, not a silent one. NO HEAP, NO LOCAL ARRAYS, NO ALLOCATION ANYWHERE. Every routine works in scalar locals and writes through caller-owned pointers. Two reasons, both estate law: this is hot-loop code and allocating in a hot loop is a measured defect; and the estate's only allocation idiom is sys_mmap, which a pure math lib must not need. Every routine that could alias its output with an input reads all operands into locals FIRST. ALL INTEGER. The language has no float type, so every result here is bit-exact and reproducible by construction. license_tier: ORIGINAL