"""Exact-arithmetic tests for points and vectors.

Oracles are hand-derived from the geometry defined in FreeRouting's
``geometry/planar/{IntPoint,IntVector,RationalPoint,RationalVector}.java``.
Emphasis is on exactness: collinearity, large coordinates that would overflow a
Java ``long``, and rational equality.
"""

from __future__ import annotations

from freeroute.geometry import (
    IntPoint,
    IntVector,
    RationalPoint,
    RationalVector,
    Side,
    Signum,
    point,
    rational_point,
)

# --- IntVector determinant / side_of ----------------------------------------


def test_determinant_exact():
    # determinant of (1,0),(0,1) = 1
    assert IntVector(1, 0).determinant(IntVector(0, 1)) == 1
    assert IntVector(0, 1).determinant(IntVector(1, 0)) == -1
    assert IntVector(2, 3).determinant(IntVector(4, 6)) == 0  # parallel


def test_determinant_exact_beyond_java_long():
    # 10**12 * 10**12 = 10**24 overflows a Java long (~9.2e18); Python int is exact.
    a = IntVector(10**12, 0)
    b = IntVector(0, 10**12)
    assert a.determinant(b) == 10**24


def test_side_of_collinear_left_right():
    # line from origin toward (1,0): +y is left, -y is right, on axis collinear.
    right_dir = IntVector(1, 0)
    assert IntVector(0, 1).side_of(right_dir) == Side.ON_THE_LEFT
    assert IntVector(0, -1).side_of(right_dir) == Side.ON_THE_RIGHT
    assert IntVector(5, 0).side_of(right_dir) == Side.COLLINEAR


def test_side_of_exact_near_collinear():
    # (10**9, 10**9) vs (10**9, 10**9 + 1): a hair off collinear, exact int detects it.
    base = IntVector(10**9, 10**9)
    assert IntVector(10**9, 10**9 + 1).side_of(base) != Side.COLLINEAR
    assert IntVector(2 * 10**9, 2 * 10**9).side_of(base) == Side.COLLINEAR


def test_vector_add_and_negate():
    assert IntVector(1, 2).add(IntVector(3, 4)) == IntVector(4, 6)
    assert IntVector(1, 2).negate() == IntVector(-1, -2)


def test_turn_90_degree():
    v = IntVector(1, 0)
    assert v.turn_90_degree(1) == IntVector(0, 1)
    assert v.turn_90_degree(2) == IntVector(-1, 0)
    assert v.turn_90_degree(3) == IntVector(0, -1)
    assert v.turn_90_degree(4) == IntVector(1, 0)
    assert v.turn_90_degree(-1) == IntVector(0, -1)


def test_projection_signum():
    assert IntVector(1, 0).projection(IntVector(1, 0)) == Signum.POSITIVE
    assert IntVector(1, 0).projection(IntVector(-1, 0)) == Signum.NEGATIVE
    assert IntVector(1, 0).projection(IntVector(0, 1)) == Signum.ZERO


def test_orthogonal_diagonal():
    assert IntVector(3, 0).is_orthogonal()
    assert IntVector(0, -4).is_orthogonal()
    assert IntVector(2, 2).is_diagonal()
    assert IntVector(-5, 5).is_diagonal()
    assert IntVector(1, 2).is_multiple_of_45_degree() is False


# --- IntPoint ---------------------------------------------------------------


def test_point_difference_and_translate():
    p = IntPoint(3, 4)
    q = IntPoint(1, 1)
    d = p.difference_by(q)
    assert isinstance(d, IntVector)
    assert d == IntVector(2, 3)
    assert q.translate_by(d) == p


def test_point_side_of_directed_line():
    p0 = IntPoint(0, 0)
    p1 = IntPoint(2, 2)
    assert IntPoint(1, 1).side_of(p0, p1) == Side.COLLINEAR
    assert IntPoint(0, 1).side_of(p0, p1) == Side.ON_THE_LEFT
    assert IntPoint(1, 0).side_of(p0, p1) == Side.ON_THE_RIGHT


def test_point_compare():
    assert IntPoint(1, 5).compare_x(IntPoint(3, 2)) == -1
    assert IntPoint(3, 5).compare_x(IntPoint(3, 2)) == 0
    assert IntPoint(3, 5).compare_y(IntPoint(3, 2)) == 1
    assert IntPoint(3, 2).compare_x_y(IntPoint(3, 5)) == -1  # x tie, y smaller


def test_point_turn_90_around_pole():
    pole = IntPoint(1, 1)
    # (2,1) rotated 90 about (1,1) -> (1,2)
    assert IntPoint(2, 1).turn_90_degree(1, pole) == IntPoint(1, 2)


# --- RationalPoint / factory ------------------------------------------------


def test_rational_point_equality_scale_invariant():
    assert RationalPoint(3, 2, 2) == RationalPoint(6, 4, 4)
    assert RationalPoint(3, 2, 2) != RationalPoint(3, 2, 3)


def test_rational_point_negative_denominator_normalized_via_factory():
    p = rational_point(3, 2, -2)  # -> (−3/−2)=... factory flips sign -> (-3,-2,2)
    assert isinstance(p, RationalPoint)
    assert p == RationalPoint(-3, -2, 2)


def test_rational_point_reduces_to_int_when_divisible():
    p = rational_point(6, 4, 2)
    assert isinstance(p, IntPoint)
    assert p == IntPoint(3, 2)


def test_rational_point_infinite():
    inf = rational_point(1, 1, 0)
    assert isinstance(inf, RationalPoint)
    assert inf.is_infinite()


def test_rational_point_contained_in_box_exact():
    from freeroute.geometry import IntBox

    box = IntBox(0, 0, 2, 2)
    assert RationalPoint(3, 2, 2).is_contained_in(box)  # (1.5, 1.0) inside
    assert not RationalPoint(5, 2, 2).is_contained_in(box)  # (2.5, 1.0) outside


def test_int_and_rational_difference_promotes():
    p = IntPoint(2, 2)
    q = RationalPoint(3, 2, 2)  # (1.5, 1.0)
    d = p.difference_by(q)
    assert isinstance(d, RationalVector)
    # (2,2) - (1.5,1.0) = (0.5, 1.0) == (1,2,2)
    assert d == RationalVector(1, 2, 2)


def test_factory_point_is_intpoint_even_for_huge_coords():
    p = point(10**15, -(10**15))
    assert isinstance(p, IntPoint)
    assert (p.x, p.y) == (10**15, -(10**15))