nx_icbrt.nx

nx_icbrt.nx -- bits-up integer cube root + Q14 fixed-point wrapper. Returns floor(cube_root(n)) for n >= 0; 0 for n < 0. Algorithm: bit-by-bit, analogous to nx_isqrt. Iterate from the highest possible bit of the cube root down; at each bit, try setting it and check whether candidate^3 still fits within n. Why this exists (substrate-level motivation, 2026-05-19): Q14 fixed-point cube root is needed for unit-exact bending mechanics in nx_pillar_physics v2.1 (the EXCEED axis vs Orca/Bambu/Cura/Prusa which use constant pillar diameter regardless of load). Square pillar bending stress: σ = M × (s/2) / I where I = s⁴/12 yields the textbook formula s = ∛(6M / σ_yield). No production slicer implements this; no academic system implements it at slice-time. Cube root has uses beyond pillar sizing -- volumetric flow at the extruder (radius scales as cbrt of flow per area), surface-area / volume ratios for cooling models, etc. Ships as a general bits-up math primitive that any future arc can compose. Overflow safety: for i64 inputs the cube root fits in 22 bits (since cube_root(2^63) ≈ 2.1e21 < 2^22 = 4.2e21). At candidate ≈ 2^21, candidate^2 ≈ 2^42 and the test candidate^3 ≤ n is rewritten as candidate^2 ≤ n / candidate to keep all intermediates in i64. license_tier: ORIGINAL