nx_fixq30_lib.nx

nx_fixq30_lib.nx -- Q30 FIXED-POINT MATH: exact multiply and divide, sqrt, CORDIC sin/cos/atan2, exp, ln, pow, cbrt. (2026-08-24, the phototwin PT1 keystone.) license_tier: ORIGINAL No hw writes (Rule 26). WHY Q30 AND WHY A NEW LIB. The estate's math primitives are Q10/Q14 (nx_trig, nx_exp, nx_icbrt, nx_isqrt_q10), ~1e-3 to 6e-5 precision, built for attention kernels and rendering. CIEDE2000 is published to four decimals (Sharma, Wu, Dalal 2005, Table I) and a hue error of 1e-4 rad on a chroma of 100 is already 0.01 dE00, so a colour ruler needs ~1e-8 arithmetic. Q30 (unit 9.3e-10) on i64 leaves 33 integer bits: every CIELAB quantity (|L|,|a|,|b| <= 200, C^2 <= 4e4) fits with room for the CORDIC gain. Those libs also carry a main() and so cannot be imported (double-main), which is why fq_isqrt is a second copy of the digit-by-digit integer sqrt -- declared here, not hidden. NO FLOATING POINT, NO TYPED-IN CONSTANTS. Every number below is a power of two, a formula integer (Machin's 5 and 239, the atanh argument 3 for ln 2), or DERIVED at runtime by series (pi, ln 2, the CORDIC atan table, the CORDIC gain). Nothing is copied from a calculator, so nothing can be mistyped; the gate KATs pi and e against their published digits as the ORACLE, which is what a KAT is for. CONTEXT: fq_ctx() computes the derived constants ONCE and hands back an i64 slot table; every trig/exp/ln call takes it. Slots: [FQ_C_PI] pi, [FQ_C_LN2] ln 2, [FQ_C_GAIN] CORDIC gain K, [FQ_C_ATAN0 + i] atan(2^-i). DOMAINS (each proven at the function): fq_mul is EXACT for |a|,|b| < 2^46 (65536 real); fq_div for |b| < 2^47 and |a/b| < 2^33 real; fq_exp saturates to FQ_SAT above x = 22.18 and underflows to 0 below x = -42.9.