nx_sketch_geomean.nx

sketch_geomean.nx -- streaming geometric mean via log-space accumulation. Geometric mean = (Π x_i)^(1/n) = 2^((Σ log_2 x_i) / n) Naive product overflows immediately (n=20, x=10 -> product ~ 10^20 >> i64). We accumulate in log_2 domain instead: log space is additive and bounded. USE CASES (where geometric mean beats arithmetic mean): - growth-rate averaging (CAGR / compound returns) - ratios (speedup factors, multiplicative gain) - normalized scores (e.g., averaging across scales) - magnitude data (sizes, populations, intensities) INTEGER LOG-BASE-2 (no f64): floor(log_2(x)) via bit_length(x) - 1 For finer fractional bits, mantissa interpolation could be added (queued for v2). SUM_LOG_2 fixed-point: track in PPM scale. Each insert contributes (bitlen - 1) * 1_000_000. Geometric mean recovered via 2^(sum/n_ppm). For 2^x where x is in PPM (fractional log_2): floor(x / 1_000_000) + linear interpolation on the fractional part. Returns approximate geometric mean. LOSSLESS-LANGUAGE DISCIPLINE: NX_ENV_REL_STDDEV with param_a reflecting quantization (use 50_000_000 ppb = 5% as conservative bound for floor-log estimator). ReferenceImpl tier.