"""CPU tests of the Dütsch protocol arithmetic (docs/validation/duetsch_re100_kc5_protocol.md §6a)."""
import importlib.util
import math
from pathlib import Path

import numpy as np
import pytest

_spec = importlib.util.spec_from_file_location(
    "duetsch_protocol", Path(__file__).resolve().parents[2] / "research/duetsch_re100_kc5/protocol.py")
p = importlib.util.module_from_spec(_spec)
_spec.loader.exec_module(p)

T = 2520


def test_phase_and_cycle_bookkeeping():
    assert p.phase(0, T) == 270.0 and p.cycle(0, T) == 0          # +A, at rest, phi = -90
    assert p.phase(T // 4, T) == 0.0 and p.cycle(T // 4, T) == 1  # mean position, u = -U_max
    assert p.position(0, T, 1.0) == 1.0
    assert p.cycle(T // 4 - 1, T) == 0 and p.cycle(T // 4 + T - 1, T) == 1
    assert p.cycle(T // 4 + T, T) == 2
    assert p.phase(T // 6, T) == pytest.approx(330.0) and p.cycle(T // 6, T) == 0  # startup quarter
    assert p.phase(7 * T // 6, T) == pytest.approx(330.0) and p.cycle(7 * T // 6, T) == 1
    for ph, frac in ((180.0, .75), (210.0, 5 / 6)):
        s = round(frac * T) + T
        assert p.phase(s, T) == pytest.approx(ph) and p.bin_phase(s, T) == ph
    assert p.bin_phase(round(.75 * T) + T - 1, T) is None
    assert sum(p.bin_phase(s, T) == 180.0 for s in range(T, 2 * T)) == T // 360


def test_settling_and_common_window():
    passes = {k: True for k in range(3, 12)}
    assert p.settled_start(passes) == 7                          # pairs 3->4, 4->5, 5->6
    late = dict(passes, **{5: False})
    assert p.settled_start(late) == 9                            # pairs 6->7, 7->8, 8->9
    assert p.common_window([7, 9], [passes, passes]) == (9, 10, 11)
    assert p.common_window([7, 10], [passes, passes]) is None    # K + 2 = 12 beyond the cap
    assert p.common_window([7, None], [passes, passes]) is None
    assert p.common_window([7, 7], [passes, dict(passes, **{8: False})]) is None  # must stay settled
    # a case settled early must keep passing while waiting for the common K
    assert p.common_window([7, 9], [dict(passes, **{8: False}), passes]) is None


def test_solid_aware_bilinear():
    field = np.arange(16.0).reshape(4, 4)
    fluid = np.ones((4, 4), bool)
    value, used, total = p.bilinear_fluid(field, fluid, 1.25, 1.5)
    assert total == pytest.approx(1.0) and value == pytest.approx(0.75 * 0.5 * (5 + 9) + 0.25 * 0.5 * (6 + 10))
    fluid[1, 1] = False                                           # one solid corner
    value, used, total = p.bilinear_fluid(field, fluid, 1.25, 1.5)
    assert total == pytest.approx(1.0 - 0.75 * 0.5)
    assert all(not (i == 1 and j == 1) for i, j, _ in used)
    assert sum(w for *_, w in used) == pytest.approx(1.0)
    fluid[:] = False
    assert p.bilinear_fluid(field, fluid, 1.25, 1.5) == (None, (), 0.0)


def test_interval_bases_and_morison_fit_recover_known_coefficients():
    b = np.array([p.interval_bases(n, T) for n in range(T // 4, T // 4 + 3 * T)])
    phi = 2 * np.pi * (np.arange(T // 4, T // 4 + 3 * T) + .5) / T - np.pi / 2
    assert np.allclose(b[:, 1], np.sin(phi), atol=1e-5)          # midpoint ~ interval mean
    f = 2.09 * b[:, 0] - (math.pi ** 2 * 1.45 / p.KC) * b[:, 1]
    assert p.morison_fit(f, b[:, 0], b[:, 1]) == pytest.approx((2.09, 1.45), abs=1e-9)


def test_geometry_repeats_exactly_across_cycles():
    A = p.amplitude(20)
    for m in (0, 1, T // 4, T // 2 - 1, 7 * T // 12):
        for c in (1, 5, 11):
            assert p.position(m + c * T, T, A) == p.position(m, T, A)
            assert p.phase(m + c * T, T) == p.phase(m, T)
            v0 = p.position(m + 1, T, A) - p.position(m, T, A)
            assert p.position(m + 1 + c * T, T, A) - p.position(m + c * T, T, A) == v0
    assert p.cycle(T // 4 + 5 * T, T) == 6  # unwrapped index stays separate
    assert p.interval_bases(123 + 7 * T, T) == p.interval_bases(123, T)


def test_exact_point_inside_body_is_missing_even_with_fluid_corners():
    field = np.zeros((6, 6))
    fluid = np.ones((6, 6), bool)
    fluid[3, 3] = False                         # only one corner solid
    centre, radius = (3.0, 3.0), 0.3
    value, used, total = p.sample(field, fluid, 3.2, 3.1, centre, radius)   # inside the circle
    assert value is None and used == () and total == 0.0
    value, used, total = p.sample(field, fluid, 3.35, 3.0, centre, radius)  # just outside
    assert value is not None and total > 0.0