"""Limit check: an infinite half-life (stock frozen at the no-AI path) must equal eps = 0 in the
paper's instantaneous rule, run for run and month by month, to within 1e-12. It is not bitwise:
the frozen run carries forward the stock the capital market cleared at, a bisection root accurate
to about 1e-16, rather than exactly 1.

Usage: python -I frozen_check.py PKG_DIR
"""
import math
import sys
from dataclasses import replace

sys.path.insert(0, sys.argv[1])
from econ_scenarios import EXTREME, MODEST, SUBSTANTIAL, Calibration, simulate  # noqa: E402

worst, identical, n = 0.0, True, 0
for s in (MODEST, SUBSTANTIAL, EXTREME):
    for xi in (0.0, 0.5, 0.9):
        cal = replace(Calibration(), xi=xi)
        frozen = simulate(s, cal, capital_half_life=math.inf).series
        eps0 = simulate(s, replace(cal, eps=0.0)).series
        n += 1
        for name in frozen:
            for x, y in zip(frozen[name], eps0[name], strict=True):
                if x != y and not (math.isnan(x) and math.isnan(y)):
                    identical = False
                    worst = max(worst, abs(x - y))
print(f"runs compared: {n}; bitwise identical: {identical}; largest abs difference: {worst:.3g}")
print("PASS (within 1e-12)" if worst <= 1e-12 else "FAIL")
sys.exit(0 if worst <= 1e-12 else 1)