from test.support import requires_IEEE_754, cpython_only
from test.test_math import parse_testfile, test_file
import test.test_math as test_math
import unittest
import cmath, math
from cmath import phase, polar, rect, pi
import platform
import sys


INF = float('inf')
NAN = float('nan')

complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]
complex_infinities = [complex(x, y) for x, y in [
        (INF, 0.0),  # 1st quadrant
        (INF, 2.3),
        (INF, INF),
        (2.3, INF),
        (0.0, INF),
        (-0.0, INF), # 2nd quadrant
        (-2.3, INF),
        (-INF, INF),
        (-INF, 2.3),
        (-INF, 0.0),
        (-INF, -0.0), # 3rd quadrant
        (-INF, -2.3),
        (-INF, -INF),
        (-2.3, -INF),
        (-0.0, -INF),
        (0.0, -INF), # 4th quadrant
        (2.3, -INF),
        (INF, -INF),
        (INF, -2.3),
        (INF, -0.0)
        ]]
complex_nans = [complex(x, y) for x, y in [
        (NAN, -INF),
        (NAN, -2.3),
        (NAN, -0.0),
        (NAN, 0.0),
        (NAN, 2.3),
        (NAN, INF),
        (-INF, NAN),
        (-2.3, NAN),
        (-0.0, NAN),
        (0.0, NAN),
        (2.3, NAN),
        (INF, NAN)
        ]]

class CMathTests(unittest.TestCase):
    # list of all functions in cmath
    test_functions = [getattr(cmath, fname) for fname in [
            'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',
            'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',
            'sqrt', 'tan', 'tanh']]
    # test first and second arguments independently for 2-argument log
    test_functions.append(lambda x : cmath.log(x, 1729. + 0j))
    test_functions.append(lambda x : cmath.log(14.-27j, x))

    def setUp(self):
        self.test_values = open(test_file)

    def tearDown(self):
        self.test_values.close()

    def assertFloatIdentical(self, x, y):
        """Fail unless floats x and y are identical, in the sense that:
        (1) both x and y are nans, or
        (2) both x and y are infinities, with the same sign, or
        (3) both x and y are zeros, with the same sign, or
        (4) x and y are both finite and nonzero, and x == y

        """
        msg = 'floats {!r} and {!r} are not identical'

        if math.isnan(x) or math.isnan(y):
            if math.isnan(x) and math.isnan(y):
                return
        elif x == y:
            if x != 0.0:
                return
            # both zero; check that signs match
            elif math.copysign(1.0, x) == math.copysign(1.0, y):
                return
            else:
                msg += ': zeros have different signs'
        self.fail(msg.format(x, y))

    def assertComplexIdentical(self, x, y):
        """Fail unless complex numbers x and y have equal values and signs.

        In particular, if x and y both have real (or imaginary) part
        zero, but the zeros have different signs, this test will fail.

        """
        self.assertFloatIdentical(x.real, y.real)
        self.assertFloatIdentical(x.imag, y.imag)

    def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,
                           msg=None):
        """Fail if the two floating-point numbers are not almost equal.

        Determine whether floating-point values a and b are equal to within
        a (small) rounding error.  The default values for rel_err and
        abs_err are chosen to be suitable for platforms where a float is
        represented by an IEEE 754 double.  They allow an error of between
        9 and 19 ulps.
        """

        # special values testing
        if math.isnan(a):
            if math.isnan(b):
                return
            self.fail(msg or '{!r} should be nan'.format(b))

        if math.isinf(a):
            if a == b:
                return
            self.fail(msg or 'finite result where infinity expected: '
                      'expected {!r}, got {!r}'.format(a, b))

        # if both a and b are zero, check whether they have the same sign
        # (in theory there are examples where it would be legitimate for a
        # and b to have opposite signs; in practice these hardly ever
        # occur).
        if not a and not b:
            if math.copysign(1., a) != math.copysign(1., b):
                self.fail(msg or 'zero has wrong sign: expected {!r}, '
                          'got {!r}'.format(a, b))

        # if a-b overflows, or b is infinite, return False.  Again, in
        # theory there are examples where a is within a few ulps of the
        # max representable float, and then b could legitimately be
        # infinite.  In practice these examples are rare.
        try:
            absolute_error = abs(b-a)
        except OverflowError:
            pass
        else:
            # test passes if either the absolute error or the relative
            # error is sufficiently small.  The defaults amount to an
            # error of between 9 ulps and 19 ulps on an IEEE-754 compliant
            # machine.
            if absolute_error <= max(abs_err, rel_err * abs(a)):
                return
        self.fail(msg or
                  '{!r} and {!r} are not sufficiently close'.format(a, b))

    def test_constants(self):
        e_expected = 2.71828182845904523536
        pi_expected = 3.14159265358979323846
        self.assertAlmostEqual(cmath.pi, pi_expected, places=9,
            msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))
        self.assertAlmostEqual(cmath.e, e_expected, places=9,
            msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))

    def test_infinity_and_nan_constants(self):
        self.assertEqual(cmath.inf.real, math.inf)
        self.assertEqual(cmath.inf.imag, 0.0)
        self.assertEqual(cmath.infj.real, 0.0)
        self.assertEqual(cmath.infj.imag, math.inf)

        self.assertTrue(math.isnan(cmath.nan.real))
        self.assertEqual(cmath.nan.imag, 0.0)
        self.assertEqual(cmath.nanj.real, 0.0)
        self.assertTrue(math.isnan(cmath.nanj.imag))

        # Check consistency with reprs.
        self.assertEqual(repr(cmath.inf), "inf")
        self.assertEqual(repr(cmath.infj), "infj")
        self.assertEqual(repr(cmath.nan), "nan")
        self.assertEqual(repr(cmath.nanj), "nanj")

    def test_user_object(self):
        # Test automatic calling of __complex__ and __float__ by cmath
        # functions

        # some random values to use as test values; we avoid values
        # for which any of the functions in cmath is undefined
        # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow
        cx_arg = 4.419414439 + 1.497100113j
        flt_arg = -6.131677725

        # a variety of non-complex numbers, used to check that
        # non-complex return values from __complex__ give an error
        non_complexes = ["not complex", 1, 5, 2., None,
                         object(), NotImplemented]

        # Now we introduce a variety of classes whose instances might
        # end up being passed to the cmath functions

        # usual case: new-style class implementing __complex__
        class MyComplex(object):
            def __init__(self, value):
                self.value = value
            def __complex__(self):
                return self.value

        # old-style class implementing __complex__
        class MyComplexOS:
            def __init__(self, value):
                self.value = value
            def __complex__(self):
                return self.value

        # classes for which __complex__ raises an exception
        class SomeException(Exception):
            pass
        class MyComplexException(object):
            def __complex__(self):
                raise SomeException
        class MyComplexExceptionOS:
            def __complex__(self):
                raise SomeException

        # some classes not providing __float__ or __complex__
        class NeitherComplexNorFloat(object):
            pass
        class NeitherComplexNorFloatOS:
            pass
        class Index:
            def __int__(self): return 2
            def __index__(self): return 2
        class MyInt:
            def __int__(self): return 2

        # other possible combinations of __float__ and __complex__
        # that should work
        class FloatAndComplex(object):
            def __float__(self):
                return flt_arg
            def __complex__(self):
                return cx_arg
        class FloatAndComplexOS:
            def __float__(self):
                return flt_arg
            def __complex__(self):
                return cx_arg
        class JustFloat(object):
            def __float__(self):
                return flt_arg
        class JustFloatOS:
            def __float__(self):
                return flt_arg

        for f in self.test_functions:
            # usual usage
            self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))
            self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))
            # other combinations of __float__ and __complex__
            self.assertEqual(f(FloatAndComplex()), f(cx_arg))
            self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))
            self.assertEqual(f(JustFloat()), f(flt_arg))
            self.assertEqual(f(JustFloatOS()), f(flt_arg))
            self.assertEqual(f(Index()), f(int(Index())))
            # TypeError should be raised for classes not providing
            # either __complex__ or __float__, even if they provide
            # __int__ or __index__.  An old-style class
            # currently raises AttributeError instead of a TypeError;
            # this could be considered a bug.
            self.assertRaises(TypeError, f, NeitherComplexNorFloat())
            self.assertRaises(TypeError, f, MyInt())
            self.assertRaises(Exception, f, NeitherComplexNorFloatOS())
            # non-complex return value from __complex__ -> TypeError
            for bad_complex in non_complexes:
                self.assertRaises(TypeError, f, MyComplex(bad_complex))
                self.assertRaises(TypeError, f, MyComplexOS(bad_complex))
            # exceptions in __complex__ should be propagated correctly
            self.assertRaises(SomeException, f, MyComplexException())
            self.assertRaises(SomeException, f, MyComplexExceptionOS())

    def test_input_type(self):
        # ints should be acceptable inputs to all cmath
        # functions, by virtue of providing a __float__ method
        for f in self.test_functions:
            for arg in [2, 2.]:
                self.assertEqual(f(arg), f(arg.__float__()))

        # but strings should give a TypeError
        for f in self.test_functions:
            for arg in ["a", "long_string", "0", "1j", ""]:
                self.assertRaises(TypeError, f, arg)

    def test_cmath_matches_math(self):
        # check that corresponding cmath and math functions are equal
        # for floats in the appropriate range

        # test_values in (0, 1)
        test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]

        # test_values for functions defined on [-1., 1.]
        unit_interval = test_values + [-x for x in test_values] + \
            [0., 1., -1.]

        # test_values for log, log10, sqrt
        positive = test_values + [1.] + [1./x for x in test_values]
        nonnegative = [0.] + positive

        # test_values for functions defined on the whole real line
        real_line = [0.] + positive + [-x for x in positive]

        test_functions = {
            'acos' : unit_interval,
            'asin' : unit_interval,
            'atan' : real_line,
            'cos' : real_line,
            'cosh' : real_line,
            'exp' : real_line,
            'log' : positive,
            'log10' : positive,
            'sin' : real_line,
            'sinh' : real_line,
            'sqrt' : nonnegative,
            'tan' : real_line,
            'tanh' : real_line}

        for fn, values in test_functions.items():
            float_fn = getattr(math, fn)
            complex_fn = getattr(cmath, fn)
            for v in values:
                z = complex_fn(v)
                self.rAssertAlmostEqual(float_fn(v), z.real)
                self.assertEqual(0., z.imag)

        # test two-argument version of log with various bases
        for base in [0.5, 2., 10.]:
            for v in positive:
                z = cmath.log(v, base)
                self.rAssertAlmostEqual(math.log(v, base), z.real)
                self.assertEqual(0., z.imag)

    @requires_IEEE_754
    def test_specific_values(self):
        # Some tests need to be skipped on ancient OS X versions.
        # See issue #27953.
        SKIP_ON_TIGER = {'tan0064'}

        osx_version = None
        if sys.platform == 'darwin':
            version_txt = platform.mac_ver()[0]
            try:
                osx_version = tuple(map(int, version_txt.split('.')))
            except ValueError: