"""Verify the Settings → Rates fixed-mode arithmetic.

For 100% stocks with growth=6% and dividend=2.5%, inflation=3%, the
expected real return per year is ``(1 + 0.06 + 0.025) / 1.03 - 1``
≈ 0.0534. We assert the simulator's portfolio compounds at this rate
in the absence of withdrawals (spending=0, no strategy draw).
"""
from __future__ import annotations

from decimal import Decimal

import numpy as np
import pytest

from fire_planner.api.schemas import SimulateRequest
from fire_planner.api.simulate import _build_paths, _project


@pytest.mark.asyncio
async def test_fixed_rates_real_return_arithmetic() -> None:
    req = SimulateRequest(
        jurisdiction="uae",  # 0% tax to isolate compounding
        strategy="trinity",
        leave_uk_year=0,
        spending_gbp=Decimal("1"),
        nw_seed_gbp=Decimal("100000"),
        horizon_years=30,
        n_paths=100,
        rates_mode="fixed",
        inflation_pct=Decimal("0.03"),
        stocks_growth_pct=Decimal("0.06"),
        stocks_dividend_pct=Decimal("0.025"),
        bonds_growth_pct=Decimal("0.015"),
        bonds_dividend_pct=Decimal("0.035"),
        stocks_allocation=Decimal("1"),
    )
    paths = await _build_paths(req)
    assert paths.shape == (100, 30, 3)
    # nominal stock return embedded should be growth + dividend = 0.085
    assert paths[0, 0, 0] == pytest.approx(0.085)
    assert paths[0, 0, 1] == pytest.approx(0.05)
    assert paths[0, 0, 2] == pytest.approx(0.03)

    expected_real = (1 + 0.06 + 0.025) / (1 + 0.03) - 1
    assert expected_real == pytest.approx(0.0534, abs=1e-3)

    result, _ = _project(req, paths)
    # All paths identical → median == any single path. After 30 years of
    # compounding 0.0534 with the trinity 4% draw, ending NW lies in a
    # well-defined window.
    end_real = float(np.median(result.portfolio_real[:, -1]))
    assert end_real > 100_000  # grew despite the £1/y withdrawal
    growth_factor = end_real / 100_000.0
    expected_factor = (1 + expected_real)**30
    # Loose because trinity strategy still draws something each year.
    assert growth_factor == pytest.approx(expected_factor, rel=0.05)