"""Tests for Sheet 4: FX parity (Part III–IV)."""

import pytest
from fqbm.state import FQBMState
from fqbm.sheets.fx_parity import (
    covered_interest_parity_fwd,
    uncovered_interest_parity_ds,
    dornbusch_s,
    fx_pass_through_inflation,
    fx_parity_step,
    FXParams,
)


def test_cip():
    F = covered_interest_parity_fwd(1.0, 0.05, 0.03)
    assert F > 1.0
    assert abs(F - 1.0 * (1.05 / 1.03)) < 1e-6


def test_uip():
    ds = uncovered_interest_parity_ds(1.0, 0.05, 0.03)
    assert abs(ds - 0.02) < 1e-6


def test_dornbusch():
    s = dornbusch_s(1.0, 0.05, 0.03, 1.5)
    assert s > 1.0
    assert abs(s - 1.0 - 1.5 * 0.02) < 1e-6


def test_fx_pass_through():
    pi = fx_pass_through_inflation(0.1, 0.2)
    assert pi == pytest.approx(0.02)


def test_fx_parity_step():
    state = FQBMState(S=1.0)
    params = FXParams(s_star=1.0, i_d=0.05, i_f=0.03, lambda_dornbusch=2.0)
    out = fx_parity_step(state, params)
    assert out.S != 1.0
    assert out.S == pytest.approx(1.0 + 2.0 * 0.02)