"""Hand-checked unit tests for the safety-stock / reorder-point math.

Every expected value below was computed by hand from the formulas in
app/inventory_math.py — see the arithmetic in each test's comments.
"""

import math
import sys
from pathlib import Path

import pytest

sys.path.insert(0, str(Path(__file__).resolve().parent.parent))
from app.inventory_math import (
    Z_90,
    demand_std_from_quantiles,
    recommend,
    z_from_service_level,
)


class TestZFromServiceLevel:
    def test_median_is_zero(self):
        assert z_from_service_level(0.5) == pytest.approx(0.0, abs=1e-8)

    def test_95_percent(self):
        # Phi^-1(0.95) = 1.6449 (standard normal table)
        assert z_from_service_level(0.95) == pytest.approx(1.6449, abs=1e-3)

    def test_90_percent_matches_Z_90_constant(self):
        assert z_from_service_level(0.90) == pytest.approx(Z_90, abs=1e-3)

    def test_99_percent(self):
        # Phi^-1(0.99) = 2.3263
        assert z_from_service_level(0.99) == pytest.approx(2.3263, abs=1e-3)

    def test_tail_region(self):
        # 0.999 falls in the approximation's upper tail branch; Phi^-1(0.999) = 3.0902
        assert z_from_service_level(0.999) == pytest.approx(3.0902, abs=1e-3)

    @pytest.mark.parametrize("bad", [0.0, 1.0, -0.5, 1.5])
    def test_rejects_out_of_range(self, bad):
        with pytest.raises(ValueError):
            z_from_service_level(bad)


class TestDemandStd:
    def test_constant_spread(self):
        # spread = 12.816 - 10 = 2.816 every day; 2.816 / 1.2816 = 2.1972...
        p50 = [10.0, 10.0, 10.0]
        p90 = [12.816, 12.816, 12.816]
        assert demand_std_from_quantiles(p50, p90) == pytest.approx(2.816 / 1.2816, rel=1e-9)

    def test_zero_spread_means_zero_std(self):
        assert demand_std_from_quantiles([5.0, 5.0], [5.0, 5.0]) == 0.0

    def test_negative_spread_clamped_to_zero(self):
        # crossed quantiles (can happen with independently trained models) never
        # produce a negative std
        assert demand_std_from_quantiles([10.0], [8.0]) == 0.0

    def test_rejects_length_mismatch(self):
        with pytest.raises(ValueError):
            demand_std_from_quantiles([1.0, 2.0], [1.0])


class TestRecommend:
    def test_hand_checked_full_example(self):
        # 7-day horizon, p50 = 10/day, p90 = 12.5632/day everywhere:
        #   avg_daily_demand = 10
        #   demand_std = (12.5632 - 10) / 1.2816 = 2.0
        #   z(0.95) = 1.6449
        #   safety_stock = 1.6449 * 2.0 * sqrt(7) = 8.7040...
        #   reorder_point = 10 * 7 + 8.7040 = 78.7040...
        #   order_qty (inventory 20) = 78.7040 - 20 = 58.7040...
        p50 = [10.0] * 7
        p90 = [12.5632] * 7
        rec = recommend(p50, p90, current_inventory=20.0, service_level=0.95,
                        lead_time_days=7)
        expected_ss = 1.6449 * 2.0 * math.sqrt(7)
        assert rec.avg_daily_demand == pytest.approx(10.0)
        assert rec.demand_std == pytest.approx(2.0, rel=1e-9)
        assert rec.safety_stock == pytest.approx(expected_ss, abs=2e-3)
        assert rec.reorder_point == pytest.approx(70.0 + expected_ss, abs=2e-3)
        assert rec.suggested_order_qty == pytest.approx(50.0 + expected_ss, abs=2e-3)

    def test_zero_uncertainty_reduces_to_deterministic_reorder(self):
        # p90 == p50 -> no safety stock; reorder point is just demand * lead time
        rec = recommend([4.0] * 7, [4.0] * 7, current_inventory=0.0,
                        service_level=0.95, lead_time_days=7)
        assert rec.safety_stock == 0.0
        assert rec.reorder_point == pytest.approx(28.0)
        assert rec.suggested_order_qty == pytest.approx(28.0)

    def test_order_qty_floors_at_zero(self):
        # plenty of inventory -> no order, never negative
        rec = recommend([1.0] * 7, [1.5] * 7, current_inventory=1000.0)
        assert rec.suggested_order_qty == 0.0

    def test_only_lead_time_days_are_used(self):
        # extra forecast days beyond the lead time must not affect the answer
        base = recommend([10.0] * 7, [12.0] * 7, lead_time_days=7)
        extended = recommend([10.0] * 7 + [999.0] * 21, [12.0] * 7 + [999.0] * 21,
                             lead_time_days=7)
        assert base.reorder_point == extended.reorder_point

    def test_lead_time_scaling(self):
        # lead time 4 with constant demand: reorder = 5*4 + z*std*sqrt(4) = 20 + 2*z*std
        # p90-p50 = 1.2816 -> std = 1.0 exactly; z(0.90) = 1.2816
        rec = recommend([5.0] * 4, [6.2816] * 4, current_inventory=0.0,
                        service_level=0.90, lead_time_days=4)
        assert rec.demand_std == pytest.approx(1.0, rel=1e-9)
        assert rec.safety_stock == pytest.approx(1.2816 * 1.0 * 2.0, abs=2e-3)
        assert rec.reorder_point == pytest.approx(20.0 + 2.5632, abs=2e-3)

    def test_rejects_short_forecast(self):
        with pytest.raises(ValueError):
            recommend([1.0] * 3, [2.0] * 3, lead_time_days=7)

    def test_rejects_bad_lead_time(self):
        with pytest.raises(ValueError):
            recommend([1.0] * 7, [2.0] * 7, lead_time_days=0)