+++ /dev/null
-from test.test_support import run_unittest\r
-from test.test_math import parse_testfile, test_file\r
-import unittest\r
-import cmath, math\r
-from cmath import phase, polar, rect, pi\r
-\r
-INF = float('inf')\r
-NAN = float('nan')\r
-\r
-complex_zeros = [complex(x, y) for x in [0.0, -0.0] for y in [0.0, -0.0]]\r
-complex_infinities = [complex(x, y) for x, y in [\r
- (INF, 0.0), # 1st quadrant\r
- (INF, 2.3),\r
- (INF, INF),\r
- (2.3, INF),\r
- (0.0, INF),\r
- (-0.0, INF), # 2nd quadrant\r
- (-2.3, INF),\r
- (-INF, INF),\r
- (-INF, 2.3),\r
- (-INF, 0.0),\r
- (-INF, -0.0), # 3rd quadrant\r
- (-INF, -2.3),\r
- (-INF, -INF),\r
- (-2.3, -INF),\r
- (-0.0, -INF),\r
- (0.0, -INF), # 4th quadrant\r
- (2.3, -INF),\r
- (INF, -INF),\r
- (INF, -2.3),\r
- (INF, -0.0)\r
- ]]\r
-complex_nans = [complex(x, y) for x, y in [\r
- (NAN, -INF),\r
- (NAN, -2.3),\r
- (NAN, -0.0),\r
- (NAN, 0.0),\r
- (NAN, 2.3),\r
- (NAN, INF),\r
- (-INF, NAN),\r
- (-2.3, NAN),\r
- (-0.0, NAN),\r
- (0.0, NAN),\r
- (2.3, NAN),\r
- (INF, NAN)\r
- ]]\r
-\r
-class CMathTests(unittest.TestCase):\r
- # list of all functions in cmath\r
- test_functions = [getattr(cmath, fname) for fname in [\r
- 'acos', 'acosh', 'asin', 'asinh', 'atan', 'atanh',\r
- 'cos', 'cosh', 'exp', 'log', 'log10', 'sin', 'sinh',\r
- 'sqrt', 'tan', 'tanh']]\r
- # test first and second arguments independently for 2-argument log\r
- test_functions.append(lambda x : cmath.log(x, 1729. + 0j))\r
- test_functions.append(lambda x : cmath.log(14.-27j, x))\r
-\r
- def setUp(self):\r
- self.test_values = open(test_file)\r
-\r
- def tearDown(self):\r
- self.test_values.close()\r
-\r
- def rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323,\r
- msg=None):\r
- """Fail if the two floating-point numbers are not almost equal.\r
-\r
- Determine whether floating-point values a and b are equal to within\r
- a (small) rounding error. The default values for rel_err and\r
- abs_err are chosen to be suitable for platforms where a float is\r
- represented by an IEEE 754 double. They allow an error of between\r
- 9 and 19 ulps.\r
- """\r
-\r
- # special values testing\r
- if math.isnan(a):\r
- if math.isnan(b):\r
- return\r
- self.fail(msg or '{!r} should be nan'.format(b))\r
-\r
- if math.isinf(a):\r
- if a == b:\r
- return\r
- self.fail(msg or 'finite result where infinity expected: '\r
- 'expected {!r}, got {!r}'.format(a, b))\r
-\r
- # if both a and b are zero, check whether they have the same sign\r
- # (in theory there are examples where it would be legitimate for a\r
- # and b to have opposite signs; in practice these hardly ever\r
- # occur).\r
- if not a and not b:\r
- if math.copysign(1., a) != math.copysign(1., b):\r
- self.fail(msg or 'zero has wrong sign: expected {!r}, '\r
- 'got {!r}'.format(a, b))\r
-\r
- # if a-b overflows, or b is infinite, return False. Again, in\r
- # theory there are examples where a is within a few ulps of the\r
- # max representable float, and then b could legitimately be\r
- # infinite. In practice these examples are rare.\r
- try:\r
- absolute_error = abs(b-a)\r
- except OverflowError:\r
- pass\r
- else:\r
- # test passes if either the absolute error or the relative\r
- # error is sufficiently small. The defaults amount to an\r
- # error of between 9 ulps and 19 ulps on an IEEE-754 compliant\r
- # machine.\r
- if absolute_error <= max(abs_err, rel_err * abs(a)):\r
- return\r
- self.fail(msg or\r
- '{!r} and {!r} are not sufficiently close'.format(a, b))\r
-\r
- def test_constants(self):\r
- e_expected = 2.71828182845904523536\r
- pi_expected = 3.14159265358979323846\r
- self.assertAlmostEqual(cmath.pi, pi_expected, places=9,\r
- msg="cmath.pi is {}; should be {}".format(cmath.pi, pi_expected))\r
- self.assertAlmostEqual(cmath.e, e_expected, places=9,\r
- msg="cmath.e is {}; should be {}".format(cmath.e, e_expected))\r
-\r
- def test_user_object(self):\r
- # Test automatic calling of __complex__ and __float__ by cmath\r
- # functions\r
-\r
- # some random values to use as test values; we avoid values\r
- # for which any of the functions in cmath is undefined\r
- # (i.e. 0., 1., -1., 1j, -1j) or would cause overflow\r
- cx_arg = 4.419414439 + 1.497100113j\r
- flt_arg = -6.131677725\r
-\r
- # a variety of non-complex numbers, used to check that\r
- # non-complex return values from __complex__ give an error\r
- non_complexes = ["not complex", 1, 5L, 2., None,\r
- object(), NotImplemented]\r
-\r
- # Now we introduce a variety of classes whose instances might\r
- # end up being passed to the cmath functions\r
-\r
- # usual case: new-style class implementing __complex__\r
- class MyComplex(object):\r
- def __init__(self, value):\r
- self.value = value\r
- def __complex__(self):\r
- return self.value\r
-\r
- # old-style class implementing __complex__\r
- class MyComplexOS:\r
- def __init__(self, value):\r
- self.value = value\r
- def __complex__(self):\r
- return self.value\r
-\r
- # classes for which __complex__ raises an exception\r
- class SomeException(Exception):\r
- pass\r
- class MyComplexException(object):\r
- def __complex__(self):\r
- raise SomeException\r
- class MyComplexExceptionOS:\r
- def __complex__(self):\r
- raise SomeException\r
-\r
- # some classes not providing __float__ or __complex__\r
- class NeitherComplexNorFloat(object):\r
- pass\r
- class NeitherComplexNorFloatOS:\r
- pass\r
- class MyInt(object):\r
- def __int__(self): return 2\r
- def __long__(self): return 2L\r
- def __index__(self): return 2\r
- class MyIntOS:\r
- def __int__(self): return 2\r
- def __long__(self): return 2L\r
- def __index__(self): return 2\r
-\r
- # other possible combinations of __float__ and __complex__\r
- # that should work\r
- class FloatAndComplex(object):\r
- def __float__(self):\r
- return flt_arg\r
- def __complex__(self):\r
- return cx_arg\r
- class FloatAndComplexOS:\r
- def __float__(self):\r
- return flt_arg\r
- def __complex__(self):\r
- return cx_arg\r
- class JustFloat(object):\r
- def __float__(self):\r
- return flt_arg\r
- class JustFloatOS:\r
- def __float__(self):\r
- return flt_arg\r
-\r
- for f in self.test_functions:\r
- # usual usage\r
- self.assertEqual(f(MyComplex(cx_arg)), f(cx_arg))\r
- self.assertEqual(f(MyComplexOS(cx_arg)), f(cx_arg))\r
- # other combinations of __float__ and __complex__\r
- self.assertEqual(f(FloatAndComplex()), f(cx_arg))\r
- self.assertEqual(f(FloatAndComplexOS()), f(cx_arg))\r
- self.assertEqual(f(JustFloat()), f(flt_arg))\r
- self.assertEqual(f(JustFloatOS()), f(flt_arg))\r
- # TypeError should be raised for classes not providing\r
- # either __complex__ or __float__, even if they provide\r
- # __int__, __long__ or __index__. An old-style class\r
- # currently raises AttributeError instead of a TypeError;\r
- # this could be considered a bug.\r
- self.assertRaises(TypeError, f, NeitherComplexNorFloat())\r
- self.assertRaises(TypeError, f, MyInt())\r
- self.assertRaises(Exception, f, NeitherComplexNorFloatOS())\r
- self.assertRaises(Exception, f, MyIntOS())\r
- # non-complex return value from __complex__ -> TypeError\r
- for bad_complex in non_complexes:\r
- self.assertRaises(TypeError, f, MyComplex(bad_complex))\r
- self.assertRaises(TypeError, f, MyComplexOS(bad_complex))\r
- # exceptions in __complex__ should be propagated correctly\r
- self.assertRaises(SomeException, f, MyComplexException())\r
- self.assertRaises(SomeException, f, MyComplexExceptionOS())\r
-\r
- def test_input_type(self):\r
- # ints and longs should be acceptable inputs to all cmath\r
- # functions, by virtue of providing a __float__ method\r
- for f in self.test_functions:\r
- for arg in [2, 2L, 2.]:\r
- self.assertEqual(f(arg), f(arg.__float__()))\r
-\r
- # but strings should give a TypeError\r
- for f in self.test_functions:\r
- for arg in ["a", "long_string", "0", "1j", ""]:\r
- self.assertRaises(TypeError, f, arg)\r
-\r
- def test_cmath_matches_math(self):\r
- # check that corresponding cmath and math functions are equal\r
- # for floats in the appropriate range\r
-\r
- # test_values in (0, 1)\r
- test_values = [0.01, 0.1, 0.2, 0.5, 0.9, 0.99]\r
-\r
- # test_values for functions defined on [-1., 1.]\r
- unit_interval = test_values + [-x for x in test_values] + \\r
- [0., 1., -1.]\r
-\r
- # test_values for log, log10, sqrt\r
- positive = test_values + [1.] + [1./x for x in test_values]\r
- nonnegative = [0.] + positive\r
-\r
- # test_values for functions defined on the whole real line\r
- real_line = [0.] + positive + [-x for x in positive]\r
-\r
- test_functions = {\r
- 'acos' : unit_interval,\r
- 'asin' : unit_interval,\r
- 'atan' : real_line,\r
- 'cos' : real_line,\r
- 'cosh' : real_line,\r
- 'exp' : real_line,\r
- 'log' : positive,\r
- 'log10' : positive,\r
- 'sin' : real_line,\r
- 'sinh' : real_line,\r
- 'sqrt' : nonnegative,\r
- 'tan' : real_line,\r
- 'tanh' : real_line}\r
-\r
- for fn, values in test_functions.items():\r
- float_fn = getattr(math, fn)\r
- complex_fn = getattr(cmath, fn)\r
- for v in values:\r
- z = complex_fn(v)\r
- self.rAssertAlmostEqual(float_fn(v), z.real)\r
- self.assertEqual(0., z.imag)\r
-\r
- # test two-argument version of log with various bases\r
- for base in [0.5, 2., 10.]:\r
- for v in positive:\r
- z = cmath.log(v, base)\r
- self.rAssertAlmostEqual(math.log(v, base), z.real)\r
- self.assertEqual(0., z.imag)\r
-\r
- def test_specific_values(self):\r
- if not float.__getformat__("double").startswith("IEEE"):\r
- return\r
-\r
- def rect_complex(z):\r
- """Wrapped version of rect that accepts a complex number instead of\r
- two float arguments."""\r
- return cmath.rect(z.real, z.imag)\r
-\r
- def polar_complex(z):\r
- """Wrapped version of polar that returns a complex number instead of\r
- two floats."""\r
- return complex(*polar(z))\r
-\r
- for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):\r
- arg = complex(ar, ai)\r
- expected = complex(er, ei)\r
- if fn == 'rect':\r
- function = rect_complex\r
- elif fn == 'polar':\r
- function = polar_complex\r
- else:\r
- function = getattr(cmath, fn)\r
- if 'divide-by-zero' in flags or 'invalid' in flags:\r
- try:\r
- actual = function(arg)\r
- except ValueError:\r
- continue\r
- else:\r
- self.fail('ValueError not raised in test '\r
- '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))\r
-\r
- if 'overflow' in flags:\r
- try:\r
- actual = function(arg)\r
- except OverflowError:\r
- continue\r
- else:\r
- self.fail('OverflowError not raised in test '\r
- '{}: {}(complex({!r}, {!r}))'.format(id, fn, ar, ai))\r
-\r
- actual = function(arg)\r
-\r
- if 'ignore-real-sign' in flags:\r
- actual = complex(abs(actual.real), actual.imag)\r
- expected = complex(abs(expected.real), expected.imag)\r
- if 'ignore-imag-sign' in flags:\r
- actual = complex(actual.real, abs(actual.imag))\r
- expected = complex(expected.real, abs(expected.imag))\r
-\r
- # for the real part of the log function, we allow an\r
- # absolute error of up to 2e-15.\r
- if fn in ('log', 'log10'):\r
- real_abs_err = 2e-15\r
- else:\r
- real_abs_err = 5e-323\r
-\r
- error_message = (\r
- '{}: {}(complex({!r}, {!r}))\n'\r
- 'Expected: complex({!r}, {!r})\n'\r
- 'Received: complex({!r}, {!r})\n'\r
- 'Received value insufficiently close to expected value.'\r
- ).format(id, fn, ar, ai,\r
- expected.real, expected.imag,\r
- actual.real, actual.imag)\r
- self.rAssertAlmostEqual(expected.real, actual.real,\r
- abs_err=real_abs_err,\r
- msg=error_message)\r
- self.rAssertAlmostEqual(expected.imag, actual.imag,\r
- msg=error_message)\r
-\r
- def assertCISEqual(self, a, b):\r
- eps = 1E-7\r
- if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps:\r
- self.fail((a ,b))\r
-\r
- def test_polar(self):\r
- self.assertCISEqual(polar(0), (0., 0.))\r
- self.assertCISEqual(polar(1.), (1., 0.))\r
- self.assertCISEqual(polar(-1.), (1., pi))\r
- self.assertCISEqual(polar(1j), (1., pi/2))\r
- self.assertCISEqual(polar(-1j), (1., -pi/2))\r
-\r
- def test_phase(self):\r
- self.assertAlmostEqual(phase(0), 0.)\r
- self.assertAlmostEqual(phase(1.), 0.)\r
- self.assertAlmostEqual(phase(-1.), pi)\r
- self.assertAlmostEqual(phase(-1.+1E-300j), pi)\r
- self.assertAlmostEqual(phase(-1.-1E-300j), -pi)\r
- self.assertAlmostEqual(phase(1j), pi/2)\r
- self.assertAlmostEqual(phase(-1j), -pi/2)\r
-\r
- # zeros\r
- self.assertEqual(phase(complex(0.0, 0.0)), 0.0)\r
- self.assertEqual(phase(complex(0.0, -0.0)), -0.0)\r
- self.assertEqual(phase(complex(-0.0, 0.0)), pi)\r
- self.assertEqual(phase(complex(-0.0, -0.0)), -pi)\r
-\r
- # infinities\r
- self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi)\r
- self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi)\r
- self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi)\r
- self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2)\r
- self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2)\r
- self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2)\r
- self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2)\r
- self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4)\r
- self.assertEqual(phase(complex(INF, -2.3)), -0.0)\r
- self.assertEqual(phase(complex(INF, -0.0)), -0.0)\r
- self.assertEqual(phase(complex(INF, 0.0)), 0.0)\r
- self.assertEqual(phase(complex(INF, 2.3)), 0.0)\r
- self.assertAlmostEqual(phase(complex(INF, INF)), pi/4)\r
- self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2)\r
- self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2)\r
- self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2)\r
- self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2)\r
- self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi)\r
- self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi)\r
- self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi)\r
-\r
- # real or imaginary part NaN\r
- for z in complex_nans:\r
- self.assertTrue(math.isnan(phase(z)))\r
-\r
- def test_abs(self):\r
- # zeros\r
- for z in complex_zeros:\r
- self.assertEqual(abs(z), 0.0)\r
-\r
- # infinities\r
- for z in complex_infinities:\r
- self.assertEqual(abs(z), INF)\r
-\r
- # real or imaginary part NaN\r
- self.assertEqual(abs(complex(NAN, -INF)), INF)\r
- self.assertTrue(math.isnan(abs(complex(NAN, -2.3))))\r
- self.assertTrue(math.isnan(abs(complex(NAN, -0.0))))\r
- self.assertTrue(math.isnan(abs(complex(NAN, 0.0))))\r
- self.assertTrue(math.isnan(abs(complex(NAN, 2.3))))\r
- self.assertEqual(abs(complex(NAN, INF)), INF)\r
- self.assertEqual(abs(complex(-INF, NAN)), INF)\r
- self.assertTrue(math.isnan(abs(complex(-2.3, NAN))))\r
- self.assertTrue(math.isnan(abs(complex(-0.0, NAN))))\r
- self.assertTrue(math.isnan(abs(complex(0.0, NAN))))\r
- self.assertTrue(math.isnan(abs(complex(2.3, NAN))))\r
- self.assertEqual(abs(complex(INF, NAN)), INF)\r
- self.assertTrue(math.isnan(abs(complex(NAN, NAN))))\r
-\r
- # result overflows\r
- if float.__getformat__("double").startswith("IEEE"):\r
- self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308))\r
-\r
- def assertCEqual(self, a, b):\r
- eps = 1E-7\r
- if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps:\r
- self.fail((a ,b))\r
-\r
- def test_rect(self):\r
- self.assertCEqual(rect(0, 0), (0, 0))\r
- self.assertCEqual(rect(1, 0), (1., 0))\r
- self.assertCEqual(rect(1, -pi), (-1., 0))\r
- self.assertCEqual(rect(1, pi/2), (0, 1.))\r
- self.assertCEqual(rect(1, -pi/2), (0, -1.))\r
-\r
- def test_isnan(self):\r
- self.assertFalse(cmath.isnan(1))\r
- self.assertFalse(cmath.isnan(1j))\r
- self.assertFalse(cmath.isnan(INF))\r
- self.assertTrue(cmath.isnan(NAN))\r
- self.assertTrue(cmath.isnan(complex(NAN, 0)))\r
- self.assertTrue(cmath.isnan(complex(0, NAN)))\r
- self.assertTrue(cmath.isnan(complex(NAN, NAN)))\r
- self.assertTrue(cmath.isnan(complex(NAN, INF)))\r
- self.assertTrue(cmath.isnan(complex(INF, NAN)))\r
-\r
- def test_isinf(self):\r
- self.assertFalse(cmath.isinf(1))\r
- self.assertFalse(cmath.isinf(1j))\r
- self.assertFalse(cmath.isinf(NAN))\r
- self.assertTrue(cmath.isinf(INF))\r
- self.assertTrue(cmath.isinf(complex(INF, 0)))\r
- self.assertTrue(cmath.isinf(complex(0, INF)))\r
- self.assertTrue(cmath.isinf(complex(INF, INF)))\r
- self.assertTrue(cmath.isinf(complex(NAN, INF)))\r
- self.assertTrue(cmath.isinf(complex(INF, NAN)))\r
-\r
-\r
-def test_main():\r
- run_unittest(CMathTests)\r
-\r
-if __name__ == "__main__":\r
- test_main()\r
projects / mirror_edk2.git / blobdiff