nx_nofloat_softmax_gate.nx

nx_nofloat_softmax_gate.nx -- a SYSTEM for the HARD no-float primitive: fixed-point exp + softmax. Transformers / attention (LLM + coding-LLM) need softmax = exp(x)/sum(exp) -- but exp is a transcendental, and float exp is NON-DETERMINISTIC. This builds it from the hardware rung up in pure INTEGER Q16: exp(x) = 2^(x*log2 e); split x*log2e into integer + fraction; 2^int = bit-shift; 2^frac = a small minimax-tuned integer Horner polynomial (endpoints pinned exact). Every op is integer -> BIT-EXACT DETERMINISTIC (the no-float exceed [[nx_nofloat_exceed_gate]]). Accuracy is verified SELF-CONSISTENTLY (no float oracle): exp(0)=1, exp(-ln2)=1/2, exp(-2ln2)=1/4, and the functional equation exp(a)exp(b)= exp(a+b). Softmax determinism: forward-sum == reverse-sum, bit-identical (float cannot promise this). This is the reusable approach for fixed-point transcendentals -> unlocks no-float attention/transformers. No hw writes (Rule 26). expect_exit: 0 license_tier: ORIGINAL