nx_mathspec_atan.nx

nx_mathspec_atan.nx -- SOVEREIGN SPEC EMITTER for the ATAN kernel: every constant computed on the 120-bit bigfloat (oracle organ nx_bigfloat120_atan), written to _pm_atan_spec.nx for the MATH_KERNEL/ATAN emitter. No python. Kernel scheme (accurate-table): anchors c_j = j/8, j = 0..20. For x < 41/16 the kernel takes j = nearest(8x), t = (x - c_j)/(1 + x*c_j) (|t| <= 1/16, x - c_j Sterbenz-exact), atan(x) = A_hi[j] + (A_lo[j] + P(t)) with P an 8-coeff odd Taylor poly (truncation < 2^-64 rel). For x >= 41/16 it folds atan(x) = pi/2 - atan(1/x); there 1/x < 0.4 so the fold target sits 2 binades below the result and the transferred error is damped 4x. Layout: c[0]=one c[1]=half c[2]=eight c[3]=pi2_hi c[4]=pi2_lo c[5]=cut(41/16) c[6..26] anchors j/8 (j=0..20) c[27..47] A_hi[j] = fl(atan(j/8)) c[48..68] A_lo[j] = fl(atan(j/8) - A_hi[j]) (signed) c[69..76] poly coeffs hi-first: -1/15 1/13 -1/11 1/9 -1/7 1/5 -1/3 1 NEGATIVE literals emitted in `0 - N` form (unary-minus literal landmine). license_tier: ORIGINAL