--- /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()