import math
import torch


def find_event(interp_fn, sign0, t0, t1, event_fn, tol):
    with torch.no_grad():

        # Num iterations for the secant method until tolerance is within target.
        nitrs = torch.ceil(torch.log((t1 - t0) / tol) / math.log(2.0))

        for _ in range(nitrs.long()):
            t_mid = (t1 + t0) / 2.0
            y_mid = interp_fn(t_mid)
            sign_mid = torch.sign(event_fn(t_mid, y_mid))
            same_as_sign0 = (sign0 == sign_mid)
            t0 = torch.where(same_as_sign0, t_mid, t0)
            t1 = torch.where(same_as_sign0, t1, t_mid)
        event_t = (t0 + t1) / 2.0

    return event_t, interp_fn(event_t)


def combine_event_functions(event_fn, t0, y0):
    """
    We ensure all event functions are initially positive,
    so then we can combine them by taking a min.
    """
    with torch.no_grad():
        initial_signs = torch.sign(event_fn(t0, y0))

    def combined_event_fn(t, y):
        c = event_fn(t, y)
        return torch.min(c * initial_signs)

    return combined_event_fn