# Wilson confidence interval monitor for Rust enforcer agreement
from prometheus_client import Gauge
import math


LOWER_BOUND = Gauge(
    "arf_rust_agreement_lower_bound",
    "Lower 99.9% Wilson bound on agreement rate",
)


def wilson_lower(success, total, z=3.291):
    """
    Compute the lower bound of the Wilson confidence interval
    for a binomial proportion.

    Parameters
    ----------
    success : int
        Number of agreed evaluations.
    total : int
        Total number of shadow evaluations (agreed + diverged).
    z : float
        Z‑score for the desired confidence level (default 3.291 for 99.9%).

    Returns
    -------
    float
        Lower bound of the Wilson interval, clamped to [0, 1].
    """
    if total == 0:
        return 0.0
    p = success / total
    n = total
    denom = 1 + z**2 / n
    center = (p + z**2 / (2 * n)) / denom
    margin = z * math.sqrt(p * (1 - p) / n + z**2 / (4 * n**2)) / denom
    return max(0.0, center - margin)


def update(agreed, diverged):
    """
    Query the Prometheus agreement counters and set the lower‑bound gauge.

    This function is called periodically by the background thread started
    in the API lifespan (see `app/main.py`).

    Parameters
    ----------
    agreed : int
        Current value of `arf_rust_agreement_total{result="agreed"}`.
    diverged : int
        Current value of `arf_rust_agreement_total{result="diverged"}`.
    """
    lower = wilson_lower(agreed, agreed + diverged)
    LOWER_BOUND.set(lower)