diff -r ffa851df0825 -r 2fb8b9db1c86 symbian-qemu-0.9.1-12/python-2.6.1/Lib/test/test_cmath.py --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/symbian-qemu-0.9.1-12/python-2.6.1/Lib/test/test_cmath.py Fri Jul 31 15:01:17 2009 +0100 @@ -0,0 +1,488 @@ +from test.test_support import run_unittest +from test.test_math import parse_testfile, test_file +import unittest +import os, sys +import cmath, math +from cmath import phase, polar, rect, pi + +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) + ]] + +def almostEqualF(a, b, rel_err=2e-15, abs_err = 5e-323): + """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): + return math.isnan(b) + if math.isinf(a): + return 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: + return math.copysign(1., a) == math.copysign(1., 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: + return False + else: + return absolute_error <= max(abs_err, rel_err * abs(a)) + +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 rAssertAlmostEqual(self, a, b, rel_err = 2e-15, abs_err = 5e-323): + """Check that two floating-point numbers are almost equal.""" + + # special values testing + if math.isnan(a): + if math.isnan(b): + return + self.fail("%s should be nan" % repr(b)) + + if math.isinf(a): + if a == b: + return + self.fail("finite result where infinity excpected: " + "expected %s, got %s" % (repr(a), repr(b))) + + if not a and not b: + if math.atan2(a, -1.) != math.atan2(b, -1.): + self.fail("zero has wrong sign: expected %s, got %s" % + (repr(a), repr(b))) + + # 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. + + try: + absolute_error = abs(b-a) + except OverflowError: + pass + else: + if absolute_error <= max(abs_err, rel_err * abs(a)): + return + self.fail("%s and %s are not sufficiently close" % (repr(a), repr(b))) + + def test_constants(self): + e_expected = 2.71828182845904523536 + pi_expected = 3.14159265358979323846 + self.rAssertAlmostEqual(cmath.pi, pi_expected, 9, + "cmath.pi is %s; should be %s" % (cmath.pi, pi_expected)) + self.rAssertAlmostEqual(cmath.e, e_expected, 9, + "cmath.e is %s; should be %s" % (cmath.e, e_expected)) + + 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, 5L, 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 MyInt(object): + def __int__(self): return 2 + def __long__(self): return 2L + def __index__(self): return 2 + class MyIntOS: + def __int__(self): return 2 + def __long__(self): return 2L + def __index__(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)) + # TypeError should be raised for classes not providing + # either __complex__ or __float__, even if they provide + # __int__, __long__ 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()) + self.assertRaises(Exception, f, MyIntOS()) + # 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 and longs 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, 2L, 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) + + def test_specific_values(self): + if not float.__getformat__("double").startswith("IEEE"): + return + + def rect_complex(z): + """Wrapped version of rect that accepts a complex number instead of + two float arguments.""" + return cmath.rect(z.real, z.imag) + + def polar_complex(z): + """Wrapped version of polar that returns a complex number instead of + two floats.""" + return complex(*polar(z)) + + for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file): + arg = complex(ar, ai) + expected = complex(er, ei) + if fn == 'rect': + function = rect_complex + elif fn == 'polar': + function = polar_complex + else: + function = getattr(cmath, fn) + if 'divide-by-zero' in flags or 'invalid' in flags: + try: + actual = function(arg) + except ValueError: + continue + else: + test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai) + self.fail('ValueError not raised in test %s' % test_str) + + if 'overflow' in flags: + try: + actual = function(arg) + except OverflowError: + continue + else: + test_str = "%s: %s(complex(%r, %r))" % (id, fn, ar, ai) + self.fail('OverflowError not raised in test %s' % test_str) + + actual = function(arg) + + if 'ignore-real-sign' in flags: + actual = complex(abs(actual.real), actual.imag) + expected = complex(abs(expected.real), expected.imag) + if 'ignore-imag-sign' in flags: + actual = complex(actual.real, abs(actual.imag)) + expected = complex(expected.real, abs(expected.imag)) + + # for the real part of the log function, we allow an + # absolute error of up to 2e-15. + if fn in ('log', 'log10'): + real_abs_err = 2e-15 + else: + real_abs_err = 5e-323 + + if not (almostEqualF(expected.real, actual.real, + abs_err = real_abs_err) and + almostEqualF(expected.imag, actual.imag)): + error_message = ( + "%s: %s(complex(%r, %r))\n" % (id, fn, ar, ai) + + "Expected: complex(%r, %r)\n" % + (expected.real, expected.imag) + + "Received: complex(%r, %r)\n" % + (actual.real, actual.imag) + + "Received value insufficiently close to expected value.") + self.fail(error_message) + + def assertCISEqual(self, a, b): + eps = 1E-7 + if abs(a[0] - b[0]) > eps or abs(a[1] - b[1]) > eps: + self.fail((a ,b)) + + def test_polar(self): + self.assertCISEqual(polar(0), (0., 0.)) + self.assertCISEqual(polar(1.), (1., 0.)) + self.assertCISEqual(polar(-1.), (1., pi)) + self.assertCISEqual(polar(1j), (1., pi/2)) + self.assertCISEqual(polar(-1j), (1., -pi/2)) + + def test_phase(self): + self.assertAlmostEqual(phase(0), 0.) + self.assertAlmostEqual(phase(1.), 0.) + self.assertAlmostEqual(phase(-1.), pi) + self.assertAlmostEqual(phase(-1.+1E-300j), pi) + self.assertAlmostEqual(phase(-1.-1E-300j), -pi) + self.assertAlmostEqual(phase(1j), pi/2) + self.assertAlmostEqual(phase(-1j), -pi/2) + + # zeros + self.assertEqual(phase(complex(0.0, 0.0)), 0.0) + self.assertEqual(phase(complex(0.0, -0.0)), -0.0) + self.assertEqual(phase(complex(-0.0, 0.0)), pi) + self.assertEqual(phase(complex(-0.0, -0.0)), -pi) + + # infinities + self.assertAlmostEqual(phase(complex(-INF, -0.0)), -pi) + self.assertAlmostEqual(phase(complex(-INF, -2.3)), -pi) + self.assertAlmostEqual(phase(complex(-INF, -INF)), -0.75*pi) + self.assertAlmostEqual(phase(complex(-2.3, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(-0.0, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(0.0, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(2.3, -INF)), -pi/2) + self.assertAlmostEqual(phase(complex(INF, -INF)), -pi/4) + self.assertEqual(phase(complex(INF, -2.3)), -0.0) + self.assertEqual(phase(complex(INF, -0.0)), -0.0) + self.assertEqual(phase(complex(INF, 0.0)), 0.0) + self.assertEqual(phase(complex(INF, 2.3)), 0.0) + self.assertAlmostEqual(phase(complex(INF, INF)), pi/4) + self.assertAlmostEqual(phase(complex(2.3, INF)), pi/2) + self.assertAlmostEqual(phase(complex(0.0, INF)), pi/2) + self.assertAlmostEqual(phase(complex(-0.0, INF)), pi/2) + self.assertAlmostEqual(phase(complex(-2.3, INF)), pi/2) + self.assertAlmostEqual(phase(complex(-INF, INF)), 0.75*pi) + self.assertAlmostEqual(phase(complex(-INF, 2.3)), pi) + self.assertAlmostEqual(phase(complex(-INF, 0.0)), pi) + + # real or imaginary part NaN + for z in complex_nans: + self.assert_(math.isnan(phase(z))) + + def test_abs(self): + # zeros + for z in complex_zeros: + self.assertEqual(abs(z), 0.0) + + # infinities + for z in complex_infinities: + self.assertEqual(abs(z), INF) + + # real or imaginary part NaN + self.assertEqual(abs(complex(NAN, -INF)), INF) + self.assert_(math.isnan(abs(complex(NAN, -2.3)))) + self.assert_(math.isnan(abs(complex(NAN, -0.0)))) + self.assert_(math.isnan(abs(complex(NAN, 0.0)))) + self.assert_(math.isnan(abs(complex(NAN, 2.3)))) + self.assertEqual(abs(complex(NAN, INF)), INF) + self.assertEqual(abs(complex(-INF, NAN)), INF) + self.assert_(math.isnan(abs(complex(-2.3, NAN)))) + self.assert_(math.isnan(abs(complex(-0.0, NAN)))) + self.assert_(math.isnan(abs(complex(0.0, NAN)))) + self.assert_(math.isnan(abs(complex(2.3, NAN)))) + self.assertEqual(abs(complex(INF, NAN)), INF) + self.assert_(math.isnan(abs(complex(NAN, NAN)))) + + # result overflows + if float.__getformat__("double").startswith("IEEE"): + self.assertRaises(OverflowError, abs, complex(1.4e308, 1.4e308)) + + def assertCEqual(self, a, b): + eps = 1E-7 + if abs(a.real - b[0]) > eps or abs(a.imag - b[1]) > eps: + self.fail((a ,b)) + + def test_rect(self): + self.assertCEqual(rect(0, 0), (0, 0)) + self.assertCEqual(rect(1, 0), (1., 0)) + self.assertCEqual(rect(1, -pi), (-1., 0)) + self.assertCEqual(rect(1, pi/2), (0, 1.)) + self.assertCEqual(rect(1, -pi/2), (0, -1.)) + + def test_isnan(self): + self.failIf(cmath.isnan(1)) + self.failIf(cmath.isnan(1j)) + self.failIf(cmath.isnan(INF)) + self.assert_(cmath.isnan(NAN)) + self.assert_(cmath.isnan(complex(NAN, 0))) + self.assert_(cmath.isnan(complex(0, NAN))) + self.assert_(cmath.isnan(complex(NAN, NAN))) + self.assert_(cmath.isnan(complex(NAN, INF))) + self.assert_(cmath.isnan(complex(INF, NAN))) + + def test_isinf(self): + self.failIf(cmath.isinf(1)) + self.failIf(cmath.isinf(1j)) + self.failIf(cmath.isinf(NAN)) + self.assert_(cmath.isinf(INF)) + self.assert_(cmath.isinf(complex(INF, 0))) + self.assert_(cmath.isinf(complex(0, INF))) + self.assert_(cmath.isinf(complex(INF, INF))) + self.assert_(cmath.isinf(complex(NAN, INF))) + self.assert_(cmath.isinf(complex(INF, NAN))) + + +def test_main(): + run_unittest(CMathTests) + +if __name__ == "__main__": + test_main()