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v0.8.1
v0.8.1
https://github.com/python/cpython
Tip revision: 74f4bd53e03ded8408bcc2de67cf0f5a4ac5b1a1 authored by Barry Warsaw on 23 February 2012, 15:59:38 UTC
Bump some more copyright years (as per PEP 101), since this is the first
Bump some more copyright years (as per PEP 101), since this is the first
Tip revision: 74f4bd5
test_cmath.py
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.assertAlmostEqual(cmath.pi, pi_expected, places=9,
msg="cmath.pi is %s; should be %s" % (cmath.pi, pi_expected))
self.assertAlmostEqual(cmath.e, e_expected, places=9,
msg="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()