nx_bigfloat120_trig.nx

nx_bigfloat120_trig.nx -- SOVEREIGN trig oracle on the 120-bit bigfloat: pi by Machin's formula, sin/cos by pi/2 reduction + Taylor. No imported constants: pi = 16*atan(1/5) - 4*atan(1/239) (Machin 1706; series self-computed) Alternating series run on TWO positive accumulators (core is positive-only), subtracted once at the end -- no catastrophic cancellation (neg/pos ratio is bounded well below 1 for 1/n arguments and r <= pi/4). Self-anchor: the trig gate's phase 0 checks sin^2 + cos^2 = 1 to < 2^-110 at random points -- an internal-consistency proof that needs no external oracle. v1 domain: |x| < 2^20 (the f64 kernel's 3-part Cody-Waite validity range); huge-argument reduction (Payne-Hanek class) is a named follow-on rung. license_tier: ORIGINAL