"""R633：带时点TWR与日期MWR；限定二次多解反例的解析诊断。"""
from datetime import date
from math import isclose, prod, sqrt


def twr(segments):
    if any(start <= 0 or end < 0 for start, end in segments):
        raise ValueError("nonpositive base or negative ending value")
    return prod(end / start for start, end in segments) - 1


def xnpv(rate, flows):
    if rate <= -1:
        raise ValueError("rate must exceed -1")
    origin = flows[0][0]
    return sum(amount / (1 + rate) ** ((day-origin).days / 365)
               for day, amount in flows)


def conventional_mwr(flows):
    if not flows:
        return "invalid_empty", None
    if not any(amount for _, amount in flows):
        return "undefined_zero_flows", None
    # 日期版求解器先净额归并同一天；没有有效投资期间不报年化率。
    by_day = {}
    for day, amount in flows:
        by_day[day] = by_day.get(day, 0) + amount
    if len(by_day) < 2:
        return "undefined_zero_period", None
    flows = sorted((day, amount) for day, amount in by_day.items() if amount)
    if not flows:
        return "undefined_zero_flows", None
    if len(flows) < 2:
        return "undefined_zero_period", None
    # 只承诺负投入在先、非负回收在后的常规模式。
    amounts = [amount for _, amount in flows if amount]
    signs = [amount > 0 for amount in amounts]
    if not any(signs) or all(signs):
        return "no_root_same_sign", None
    changes = sum(a != b for a, b in zip(signs, signs[1:]))
    if changes != 1 or signs[0]:
        return "nonconventional_needs_root_analysis", None
    lo, hi = -0.9999, 10.0
    if xnpv(lo, flows) * xnpv(hi, flows) > 0:
        return "not_bracketed", None
    for _ in range(180):
        mid = (lo + hi) / 2
        if xnpv(mid, flows) > 0:
            lo = mid
        else:
            hi = mid
    rate = (lo + hi) / 2
    assert abs(xnpv(rate, flows)) < 1e-6
    return "unique_conventional", rate


def run():
    start, middle, end = date(2023, 1, 1), date(2024, 1, 1), date(2024, 12, 31)
    assert (middle-start).days == (end-middle).days == 365
    # t=1入金前110，入金90后200，t=2期末180；各相隔365天。
    opening, before, deposit, terminal = 100, 110, 90, 180
    after = before + deposit
    result = twr([(opening, before), (after, terminal)])
    status, annual = conventional_mwr([(start, -opening), (middle, -deposit), (end, terminal)])
    net_contributions = opening + deposit
    gain = terminal - net_contributions
    assert opening + deposit + gain == terminal
    assert isclose(result, -0.01, abs_tol=1e-12)
    assert status == "unique_conventional"
    assert isclose(annual, (-90 + sqrt(80100)) / 200 - 1, abs_tol=1e-12)
    # 非常规流：-100,+230,-132，令x=1+r，得到100x²-230x+132=0。
    unusual = [(start, -100), (middle, 230), (end, -132)]
    roots = sorted([(230-sqrt(100))/200-1, (230+sqrt(100))/200-1])
    assert all(abs(xnpv(rate, unusual)) < 1e-8 for rate in roots)
    assert conventional_mwr(unusual)[0] == "nonconventional_needs_root_analysis"
    no_root = conventional_mwr([(start, -100), (end, -10)])[0]
    assert no_root == "no_root_same_sign"
    assert conventional_mwr([])[0] == "invalid_empty"
    assert conventional_mwr([(start, 0)])[0] == "undefined_zero_flows"
    assert conventional_mwr([(start, -100), (start, 100)])[0] == "undefined_zero_period"
    assert conventional_mwr([(start, -100), (start, 100), (end, -10), (end, 10)])[0] == "undefined_zero_flows"
    print(f"subperiods=10.0000%,-10.0000% TWR={result:.4%}")
    print(f"gain={gain} ending={terminal} net_contributions={net_contributions} MWR_annual={annual:.6%}")
    print(f"MWR_two_year_equivalent={(1+annual)**2-1:.6%}")
    print("nonconventional_roots=10.000000%,20.000000%")
    print("same_sign_status=" + no_root)
    print("input_statuses=invalid_empty,undefined_zero_flows,undefined_zero_period")
    try:
        twr([(0, 10)])
    except ValueError:
        print("zero_base_TWR=rejected")
    else:
        raise AssertionError("zero base accepted")


if __name__ == "__main__":
    run()