"""Unit tests for basic math functions"""

# Copyright (C) 2011-2014 Martin Alnaes
#
# This file is part of DOLFIN.
#
# DOLFIN is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# DOLFIN 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 Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# Modified by Garth N. Wells, 2011

import pytest
import numpy
from dolfin import *


def test_near():
    eps = DOLFIN_EPS
    # Loop over magnitudes
    for i in range(100):
        # Loop over base values
        for j in range(1, 10):
            # Compute a value v and some values close to it
            v = float(j*10**(i-13))
            vm = v - eps
            vp = v + eps
            #vm = v - v*eps # Scaling eps does not work
            #vp = v + v*eps

            # Check that we return True when we should by definition:
            assert near(v, v)
            assert near(vm, vm)
            assert near(vp, vp)
            #assert near(v, vm) # Can fail
            #assert near(v, vp)
            if not near(v, vm):
                print("not near vm: {}, {}".format(v, vm))
            if not near(v, vp):
                print("not near vp: {}, {}".format(v, vp))

            # vm and vp can round off to v, make some small values != v
            # that are close to 1 (except for some of the smallest v's)
            v2m = v * (1.0 - 2*eps) - 2*eps
            v2p = v * (1.0 + 2*eps) + 2*eps
            assert v/v2m > 1.0
            assert v/v2p < 1.0

            # Check that we can fail for fairly close values
            assert not near(v, v2m)
            assert not near(v, v2p)

def test_between():
    eps = DOLFIN_EPS
    # Loop over magnitudes
    for i in range(100):
        # Loop over base values
        for j in range(1, 10):
            # Compute a value v and some values close to it
            v = float(j*10**(i - 15))
            vm = v - eps
            vp = v + eps

            # Check that we return True when we should by definition:
            assert between(v, (vm, vp))

            # vm and vp can round off to v, make some small values != v
            v2m = v * (1.0 - 2*eps) - 2*eps
            v2p = v * (1.0 + 2*eps) + 2*eps

            # Close to 1 except for some of the smallest v's:
            assert v/v2m > 1.0
            assert v/v2p < 1.0
            assert between(v, (v2m, v2p))

            # Check that we can fail for fairly close values
            assert not between(v, (v2p, v2m))

def test_ipow():
    with pytest.raises(RuntimeError):
        ipow(0, 0)
    assert ipow(0, 1) == 0
    assert ipow(0, 10) == 0
    assert ipow(0, 12345) == 0
    assert ipow(1, 12345) == 1
    assert ipow(12345, 0) == 1
    assert ipow(12345, 1) == 12345
    assert ipow(2, 15) == 32768

@pytest.mark.xfail
def test_ipow_overflow():
    # This will fail because of overflow in dolfin/math/basic.cpp
    # on 64-bit size_t. When __builtin_mul_overflow is employed
    # to do the check, exception will be raised instead.
    assert ipow(3, 41) == 3**41