"""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


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