#    Virtual-IPM is a software for simulating IPMs and other related devices.
#    Copyright (C) 2021  The IPMSim collaboration <https://ipmsim.gitlab.io/>
#
#    This program is free software: you can redistribute it and/or modify
#    it under the terms of the GNU Affero General Public License as
#    published by the Free Software Foundation, either version 3 of the
#    License, or (at your option) any later version.
#
#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU Affero General Public License for more details.
#
#    You should have received a copy of the GNU Affero General Public License
#    along with this program.  If not, see <http://www.gnu.org/licenses/>.

from numpy import cos, sin


def sincc(x):
    th = 1e-4  # threshold value

    if abs(x) < th:
        return 1.
    else:
        return sin(x) / x


def cosincc(x):
    th = 1e-4  # threshold value

    if abs(x) < th:
        return 0.5
    else:
        return (1 - cos(x)) / (x * x)


def cubsincc(x):
    th = 1e-4  # threshold value

    if abs(x) < th:
        return 1. / 6.
    else:
        return (x - sin(x)) / (x * x * x)
