sketch_correlation.nx

sketch_correlation.nx -- streaming Pearson correlation + linear regression. Bivariate streaming primitive. For paired observations (x, y) consumed one at a time, computes: r -- Pearson correlation coefficient, in PPM in [-1_000_000, 1_000_000] slope -- least-squares regression slope m: y = m*x + b intercept -- least-squares regression intercept b SIX ACCUMULATORS (integer-exact under overflow budget): n = count sum_x = Σ x_i sum_y = Σ y_i sum_xy = Σ x_i * y_i sum_xx = Σ x_i² sum_yy = Σ y_i² FORMULAS: cov_xy = n * sum_xy - sum_x * sum_y var_x = n * sum_xx - sum_x² var_y = n * sum_yy - sum_y² r = cov_xy / sqrt(var_x * var_y) slope = cov_xy / var_x intercept = (sum_y - slope * sum_x) / n OVERFLOW BUDGET: sum_xx grows as n * x_max². For x_max=2^15, n_max=2^32 -> sum_xx max ~ 2^62. And the cross-term computations need extra margin. nx_corr_safe_p flags unsafe inputs. USE CASES: - SRE: correlate metric series (CPU vs latency) - finance: returns correlation - science: regression on streamed measurements LOSSLESS-LANGUAGE DISCIPLINE: r returned in PPM with NX_ENV_ABS, param_a = 0 (exact under budget). Production tier.