"""Pins for PREREG_flat_regime_2026-09-21.md: the flat gate (prestep='flat')."""
from __future__ import annotations

import math

import pytest

from simroot.pure import pure_root

XTOL, MAXFEV = 1e-12, 200
PROBS = (
    (lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0),
    (lambda t: math.exp(t) - 2.0, 0.0, 3.0),
    (lambda t: 6.0 * (t - 2.0) ** 5, 0.0, 10.0),
    (lambda t: t ** 19, -10.0, 100.0),
)


@pytest.mark.parametrize("f,a,b", PROBS)
@pytest.mark.parametrize("guard", ("project", "credit", "safe"))
def test_the_default_is_untouched(f, a, b, guard):
    ref = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard)
    off = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard,
                    prestep="none")
    assert ref == off


@pytest.mark.parametrize("f,a,b", PROBS)
@pytest.mark.parametrize("guard", ("project", "credit"))
@pytest.mark.parametrize("ext", ("none", "pattern"))
def test_the_guarantee_holds_with_the_gate(f, a, b, guard, ext):
    x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
                         guard=guard, prestep="flat", extrapolate=ext)
    assert ok and min(a, b) <= x <= max(a, b)
    half = math.ceil(math.log2(abs(b - a) / XTOL))
    assert n <= (2 * half + 3 if guard == "project" else half + 4), n


@pytest.mark.parametrize("f,a,b", PROBS)
@pytest.mark.parametrize("guard", ("project", "credit"))
@pytest.mark.parametrize("ext", ("none", "pattern"))
def test_the_guarantee_holds_with_the_twice_gate(f, a, b, guard, ext):
    x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
                         guard=guard, prestep="flat2", extrapolate=ext)
    assert ok and min(a, b) <= x <= max(a, b)
    half = math.ceil(math.log2(abs(b - a) / XTOL))
    assert n <= (2 * half + 3 if guard == "project" else half + 4), n


def test_the_twice_gate_is_silent_where_the_model_is_exact_and_fires_on_a_power():
    st = {}
    pure_root(lambda t: 3.0 * t - 1.0, -2.0, 5.0, XTOL, MAXFEV, similarity="ratio",
              scale="derived3", guard="project", prestep="flat2", stats=st)
    assert st["pre_refused"] == 0
    st = {}
    pure_root(lambda t: t ** 9, -1.0, 2.0, XTOL, MAXFEV, similarity="ratio",
              scale="derived3", guard="project", prestep="flat2", stats=st)
    assert st["pre_refused"] > 0


@pytest.mark.parametrize("f,a,b", PROBS)
@pytest.mark.parametrize("guard", ("project", "credit"))
@pytest.mark.parametrize("ext", ("none", "pattern"))
def test_the_guarantee_holds_with_the_creep_gate(f, a, b, guard, ext):
    x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
                         guard=guard, prestep="flatcreep", extrapolate=ext)
    assert ok and min(a, b) <= x <= max(a, b)
    half = math.ceil(math.log2(abs(b - a) / XTOL))
    assert n <= (2 * half + 3 if guard == "project" else half + 4), n


def test_the_creep_gate_is_silent_on_a_line_fires_on_a_power_and_spares_a_simple_root():
    """Measured before pinning: silent where the model is exact, fires on x^9, and does
    NOT fire on x^3 - 2x - 5 over [1, 4], where the single flag fired once."""
    runs = {}
    for name, f, a, b in (("line", lambda t: 3.0 * t - 1.0, -2.0, 5.0),
                          ("x9", lambda t: t ** 9, -1.0, 2.0),
                          ("cubic", lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0)):
        st = {}
        pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
                  guard="project", prestep="flatcreep", stats=st)
        runs[name] = st["pre_refused"]
    assert runs["line"] == 0 and runs["x9"] > 0 and runs["cubic"] == 0, runs


def test_the_gate_never_fires_where_the_model_is_exact():
    """On a straight line the model's step lands on the root: r = 0, never >= 1/4."""
    st = {}
    pure_root(lambda t: 3.0 * t - 1.0, -2.0, 5.0, XTOL, MAXFEV, similarity="ratio",
              scale="derived3", guard="project", prestep="flat", stats=st)
    assert st["pre_refused"] == 0


def test_the_gate_fires_on_a_pure_power():
    """On x^9 the tangent step leaves (8/9)^9 = 0.35 of |f| on the same side."""
    st = {}
    pure_root(lambda t: t ** 9, -1.0, 2.0, XTOL, MAXFEV, similarity="ratio",
              scale="derived3", guard="project", prestep="flat", stats=st)
    assert st["pre_refused"] > 0