"""Firing-solution math, from High Command's gunnery tables.

Distances/bearings reuse the same board-units-are-km convention as
solver.py. Powder charge controls elevation: more charge, lower arc for
the same distance, up to MAX_POWDER_CHARGE; min_powder_charge() is the
least charge that can still reach a given distance at all.
"""

from __future__ import annotations

import math

from .models import Coord

MAX_POWDER_CHARGE = 6


def distance_km_point(a: tuple[float, float], b: tuple[float, float]) -> float:
    return math.hypot(b[0] - a[0], b[1] - a[1])


def bearing_deg_point(a: tuple[float, float], b: tuple[float, float]) -> float:
    """Compass bearing from a to b: 0 = north (+row), 90 = east (+col),
    matching solver.py's convention, the inverse of
    solver.point_from_bearing_distance()."""
    return math.degrees(math.atan2(b[0] - a[0], b[1] - a[1])) % 360


def distance_km(a: Coord, b: Coord) -> float:
    return distance_km_point(a.as_fraction(), b.as_fraction())


def bearing_deg(a: Coord, b: Coord) -> float:
    return bearing_deg_point(a.as_fraction(), b.as_fraction())


def min_powder_charge(dist_km: float, eps: float = 1e-9) -> int:
    n = dist_km / 5
    rounded = round(n)
    if abs(n - rounded) < eps:
        return max(1, rounded)
    return math.ceil(n)


def elevation_deg(dist_km: float, charges: int) -> float:
    return 12 * dist_km / charges