import math
from dataclasses import dataclass

EARTH_RADIUS_M = 6371000.0


@dataclass(frozen=True)
class GPSCoordinate:
    latitude: float
    longitude: float


def calculate_haversine_distance(coord_a: GPSCoordinate, coord_b: GPSCoordinate) -> float:
    lat_rad_a = math.radians(coord_a.latitude)
    lat_rad_b = math.radians(coord_b.latitude)
    delta_lat = math.radians(coord_b.latitude - coord_a.latitude)
    delta_lon = math.radians(coord_b.longitude - coord_a.longitude)

    haversine_term = (
        math.sin(delta_lat / 2.0) ** 2
        + math.cos(lat_rad_a) * math.cos(lat_rad_b) * (math.sin(delta_lon / 2.0) ** 2)
    )

    angular_distance = 2.0 * math.atan2(math.sqrt(haversine_term), math.sqrt(1.0 - haversine_term))
    return EARTH_RADIUS_M * angular_distance


def is_within_geofence(
    student_coord: GPSCoordinate,
    classroom_coord: GPSCoordinate,
    base_radius: float,
    student_accuracy: float,
) -> bool:
    """Validates if student is within the classroom geofence, accounting for GPS drift.

    The effective radius is the base classroom radius plus student accuracy.
    """
    distance = calculate_haversine_distance(student_coord, classroom_coord)
    effective_radius = base_radius + student_accuracy
    return distance <= effective_radius