nx_f32_sincos.nx

nx_f32_sincos.nx -- IEEE 754 binary32 sin(x) + cos(x) bits-up. L6 transcendentals. Composes L4 mul/add/sub/cvt. No libm. Algorithm (clean-room from cited refs): 1. Range reduction: k = round(x * 2/pi) r = x - k * pi/2, r in [-pi/4, pi/4] Quadrant q = k mod 4. 2. Reduced-range polynomials (Taylor, 4 odd / 4 even terms): sin(r) ~= r - r^3/6 + r^5/120 - r^7/5040 ~= r * (1 - r^2/6 + r^4/120 - r^6/5040) cos(r) ~= 1 - r^2/2 + r^4/24 - r^6/720 3. Quadrant dispatch: sin: q=0 -> sin(r) ; q=1 -> cos(r) ; q=2 -> -sin(r) ; q=3 -> -cos(r) cos: q=0 -> cos(r) ; q=1 -> -sin(r) ; q=2 -> -cos(r) ; q=3 -> sin(r) References absorbed clean-room: Hart 1968, Cody+Waite 1980, Muller 2016 Standard quadrant-based range-reduction canon v1 accuracy: ~1000-10000 ULPs (Taylor truncation + range reduction loss; classic single-word pi/2 issue). Adequate for ML positional encoding (RoPE). v2 Remez minimax + Cody-Waite split pi/2 for tighter bounds queued. genealogy_id: standard_quadrant_reduction + taylor_horner_canon lineage_id: substrate_f32_sincos_v1_taylor4