nx_bigfloat120_tan.nx

nx_bigfloat120_tan.nx -- SOVEREIGN tan oracle on the 120-bit bigfloat: tan = sin/cos over the blessed trig organ's reduction (period pi handled by the quadrant parity: k odd -> -cot). Positive-only core; the bigfloat entry point bf_tan_xb takes an UNROUNDED bigfloat argument so the self-anchor gate can test algebraic identities (half-angle, pi-shift) at full precision across DIFFERENT reduction paths -- not just at f64-rounded points. v1 domain |x| < 2^20 (the trig organ's Cody-Waite range; same honest refusal). Near poles: r >= ~2^-61 for any f64 near k*pi/2, so cot = cos/sin stays a well-conditioned bigfloat division (no overflow band in f64 tan). license_tier: ORIGINAL