nx_f32_exp.nx

nx_f32_exp.nx -- IEEE 754 binary32 exp(x) bits-up. L6 of the bits-up numeric tower. Composes L4 mul/add/sub/cvt to produce a real-valued exp(x) without libm. Algorithm (standard, no code borrowed): 1. Special cases per IEEE 754: exp(NaN) = NaN exp(+0) = +1 exp(-0) = +1 exp(+inf) = +inf exp(-inf) = +0 Overflow (x >> 88) -> +inf Underflow (x << -87) -> +0 2. Range reduction: x = k * ln(2) + r, where k is an integer and r in [-ln(2)/2, ln(2)/2] ~= [-0.347, 0.347]. k = round(x / ln(2)) r = x - k * ln(2) Then exp(x) = 2^k * exp(r). 3. Polynomial approximation of exp(r) on reduced range: Taylor through r^6 (Horner form, 6 multiplies + 6 adds). Worst-case ULP error on r in [-0.347, 0.347]: ~4-8 ULPs in f32 (deemed acceptable for ML softmax; tighter Remez minimax is a v2 lift). 4. Multiply by 2^k: add k to f32 biased exponent. Overflow -> inf; underflow to subnormal range -> conservative 0 (v1). References absorbed clean-room (no code borrowed): Hart 1968, "Computer Approximations" (range reduction + polynomial design) Cody+Waite 1980, "Software Manual for Elementary Functions" Muller 2016, "Elementary Functions: Algorithms and Implementation" genealogy_id: range_reduction_canonical + taylor_horner_form lineage_id: substrate_f32_exp_v1_taylor6