def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
#self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
#self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
#self.assertEqual(math.ldexp(1., -1000000), 0.)
#self.assertEqual(math.ldexp(-1., -1000000), -0.)
self.assertEqual(math.ldexp(INF, 30), INF)
self.assertEqual(math.ldexp(NINF, -213), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEqual(math.ldexp(INF, -n), INF)
self.assertEqual(math.ldexp(NINF, -n), NINF)
#self.assertEqual(math.ldexp(1., -n), 0.)
#self.assertEqual(math.ldexp(-1., -n), -0.)
self.assertEqual(math.ldexp(0., -n), 0.)
self.assertEqual(math.ldexp(-0., -n), -0.)
self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
#self.assertRaises(OverflowError, math.ldexp, 1., n)
#self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEqual(math.ldexp(0., n), 0.)
self.assertEqual(math.ldexp(-0., n), -0.)
self.assertEqual(math.ldexp(INF, n), INF)
self.assertEqual(math.ldexp(NINF, n), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, n)))
def testCopysign(self):
self.assertEqual(math.copysign(1, 42), 1.0)
self.assertEqual(math.copysign(0., 42), 0.0)
self.assertEqual(math.copysign(1., -42), -1.0)
self.assertEqual(math.copysign(3, 0.), 3.0)
self.assertEqual(math.copysign(4., -0.), -4.0)
self.assertRaises(TypeError, math.copysign)
# copysign should let us distinguish signs of zeros
self.assertEqual(math.copysign(1., 0.), 1.)
self.assertEqual(math.copysign(1., -0.), -1.)
self.assertEqual(math.copysign(INF, 0.), INF)
self.assertEqual(math.copysign(INF, -0.), NINF)
self.assertEqual(math.copysign(NINF, 0.), INF)
self.assertEqual(math.copysign(NINF, -0.), NINF)
# and of infinities
self.assertEqual(math.copysign(1., INF), 1.)
self.assertEqual(math.copysign(1., NINF), -1.)
self.assertEqual(math.copysign(INF, INF), INF)
self.assertEqual(math.copysign(INF, NINF), NINF)
self.assertEqual(math.copysign(NINF, INF), INF)
self.assertEqual(math.copysign(NINF, NINF), NINF)
self.assertTrue(math.isnan(math.copysign(NAN, 1.)))
self.assertTrue(math.isnan(math.copysign(NAN, INF)))
self.assertTrue(math.isnan(math.copysign(NAN, NINF)))
self.assertTrue(math.isnan(math.copysign(NAN, NAN)))
# copysign(INF, NAN) may be INF or it may be NINF, since
# we don't know whether the sign bit of NAN is set on any
# given platform.
self.assertTrue(math.isinf(math.copysign(INF, NAN)))
# similarly, copysign(2., NAN) could be 2. or -2.
self.assertEqual(abs(math.copysign(2., NAN)), 2.)
def testCopysign(self):
self.assertEqual(math.copysign(1, 42), 1.0)
self.assertEqual(math.copysign(0., 42), 0.0)
self.assertEqual(math.copysign(1., -42), -1.0)
self.assertEqual(math.copysign(3, 0.), 3.0)
self.assertEqual(math.copysign(4., -0.), -4.0)
self.assertRaises(TypeError, math.copysign)
# copysign should let us distinguish signs of zeros
self.assertEqual(math.copysign(1., 0.), 1.)
self.assertEqual(math.copysign(1., -0.), -1.)
self.assertEqual(math.copysign(INF, 0.), INF)
self.assertEqual(math.copysign(INF, -0.), NINF)
self.assertEqual(math.copysign(NINF, 0.), INF)
self.assertEqual(math.copysign(NINF, -0.), NINF)
# and of infinities
self.assertEqual(math.copysign(1., INF), 1.)
self.assertEqual(math.copysign(1., NINF), -1.)
self.assertEqual(math.copysign(INF, INF), INF)
self.assertEqual(math.copysign(INF, NINF), NINF)
self.assertEqual(math.copysign(NINF, INF), INF)
self.assertEqual(math.copysign(NINF, NINF), NINF)
self.assertTrue(math.isnan(math.copysign(NAN, 1.)))
self.assertTrue(math.isnan(math.copysign(NAN, INF)))
self.assertTrue(math.isnan(math.copysign(NAN, NINF)))
self.assertTrue(math.isnan(math.copysign(NAN, NAN)))
# copysign(INF, NAN) may be INF or it may be NINF, since
# we don't know whether the sign bit of NAN is set on any
# given platform.
self.assertTrue(math.isinf(math.copysign(INF, NAN)))
# similarly, copysign(2., NAN) could be 2. or -2.
self.assertEqual(abs(math.copysign(2., NAN)), 2.)
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
###self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
###self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
###self.assertEqual(math.ldexp(1., -1000000), 0.)
###self.assertEqual(math.ldexp(-1., -1000000), -0.)
self.assertEqual(math.ldexp(INF, 30), INF)
self.assertEqual(math.ldexp(NINF, -213), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEqual(math.ldexp(INF, -n), INF)
self.assertEqual(math.ldexp(NINF, -n), NINF)
###self.assertEqual(math.ldexp(1., -n), 0.)
###self.assertEqual(math.ldexp(-1., -n), -0.)
self.assertEqual(math.ldexp(0., -n), 0.)
self.assertEqual(math.ldexp(-0., -n), -0.)
self.assertTrue(math.isnan(math.ldexp(NAN, -n)))
###self.assertRaises(OverflowError, math.ldexp, 1., n)
###self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEqual(math.ldexp(0., n), 0.)
self.assertEqual(math.ldexp(-0., n), -0.)
self.assertEqual(math.ldexp(INF, n), INF)
self.assertEqual(math.ldexp(NINF, n), NINF)
self.assertTrue(math.isnan(math.ldexp(NAN, n)))
def checker(self,n):
fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}"
failures = []
idn=n
if n=='setattr_test':
self.assertTrue(True)
else:
fn, arg, expected, flags=self.te[n]
func = getattr(math, fn)
if 'invalid' in flags or 'divide-by-zero' in flags:
expected = 'ValueError'
elif 'overflow' in flags:
expected = 'OverflowError'
try:
got = func(arg)
except ValueError:
got = 'ValueError'
except OverflowError:
got = 'OverflowError'
accuracy_failure = None
if isinstance(got, (math.cf_base,float)) and isinstance(expected, float):
if math.isnan(expected) and math.isnan(got):
return
if not math.isnan(expected) and not math.isnan(got):
if fn == 'lgamma':
# we use a weaker accuracy test for lgamma;
# lgamma only achieves an absolute error of
# a few multiples of the machine accuracy, in
# general.
accuracy_failure = acc_check(expected, got,
rel_err = 5e-15,
abs_err = 5e-15)
elif fn == 'erfc':
# erfc has less-than-ideal accuracy for large
# arguments (x ~ 25 or so), mainly due to the
# error involved in computing exp(-x*x).
#
# XXX Would be better to weaken this test only
# for large x, instead of for all x.
accuracy_failure = ulps_check(expected, got, 2000)
else:
accuracy_failure = ulps_check(expected, got, 20)
if accuracy_failure is None:
return
if isinstance(got, str) and isinstance(expected, str):
if got == expected:
return
fail_msg = fail_fmt.format(idn, fn, arg, expected, got)
if accuracy_failure is not None:
fail_msg += ' ({})'.format(accuracy_failure)
failures.append(fail_msg)
if failures:
self.fail('Failures in test_mtestfile:\n ' + '\n '.join(failures))
def test_mtestfile(self):
ALLOWED_ERROR = 20 # permitted error, in ulps
fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}"
failures = []
for id, fn, arg, expected, flags in parse_mtestfile(math_testcases):
func = getattr(math, fn)
if 'invalid' in flags or 'divide-by-zero' in flags:
expected = 'ValueError'
elif 'overflow' in flags:
expected = 'OverflowError'
try:
got = func(arg)
except ValueError:
got = 'ValueError'
except OverflowError:
got = 'OverflowError'
accuracy_failure = None
if isinstance(got, float) and isinstance(expected, float):
if math.isnan(expected) and math.isnan(got):
continue
if not math.isnan(expected) and not math.isnan(got):
if fn == 'lgamma':
# we use a weaker accuracy test for lgamma;
# lgamma only achieves an absolute error of
# a few multiples of the machine accuracy, in
# general.
accuracy_failure = acc_check(expected, got,
rel_err = 5e-15,
abs_err = 5e-15)
elif fn == 'erfc':
# erfc has less-than-ideal accuracy for large
# arguments (x ~ 25 or so), mainly due to the
# error involved in computing exp(-x*x).
#
# XXX Would be better to weaken this test only
# for large x, instead of for all x.
accuracy_failure = ulps_check(expected, got, 2000)
else:
accuracy_failure = ulps_check(expected, got, 20)
if accuracy_failure is None:
continue
if isinstance(got, str) and isinstance(expected, str):
if got == expected:
continue
fail_msg = fail_fmt.format(id, fn, arg, expected, got)
if accuracy_failure is not None:
fail_msg += ' ({})'.format(accuracy_failure)
failures.append(fail_msg)
if failures:
self.fail('Failures in test_mtestfile:\n ' +
'\n '.join(failures))
def testHypot(self):
self.assertRaises(TypeError, math.hypot)
self.ftest('hypot(0,0)', math.hypot(0,0), 0)
self.ftest('hypot(3,4)', math.hypot(3,4), 5)
self.assertEqual(math.hypot(NAN, INF), INF)
self.assertEqual(math.hypot(INF, NAN), INF)
self.assertEqual(math.hypot(NAN, NINF), INF)
self.assertEqual(math.hypot(NINF, NAN), INF)
self.assertTrue(math.isnan(math.hypot(1.0, NAN)))
self.assertTrue(math.isnan(math.hypot(NAN, -2.0)))
def testHypot(self):
self.assertRaises(TypeError, math.hypot)
self.ftest('hypot(0,0)', math.hypot(0,0), 0)
self.ftest('hypot(3,4)', math.hypot(3,4), 5)
self.assertEqual(math.hypot(NAN, INF), INF)
self.assertEqual(math.hypot(INF, NAN), INF)
self.assertEqual(math.hypot(NAN, NINF), INF)
self.assertEqual(math.hypot(NINF, NAN), INF)
self.assertTrue(math.isnan(math.hypot(1.0, NAN)))
self.assertTrue(math.isnan(math.hypot(NAN, -2.0)))
def testSin(self):
self.assertRaises(TypeError, math.sin)
self.ftest('sin(0)', math.sin(0), 0)
self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
try:
self.assertTrue(math.isnan(math.sin(INF)))
self.assertTrue(math.isnan(math.sin(NINF)))
except ValueError:
self.assertRaises(ValueError, math.sin, INF)
self.assertRaises(ValueError, math.sin, NINF)
self.assertTrue(math.isnan(math.sin(NAN)))
def testTan(self):
self.assertRaises(TypeError, math.tan)
self.ftest('tan(0)', math.tan(0), 0)
self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
try:
self.assertTrue(math.isnan(math.tan(INF)))
self.assertTrue(math.isnan(math.tan(NINF)))
except:
self.assertRaises(ValueError, math.tan, INF)
self.assertRaises(ValueError, math.tan, NINF)
self.assertTrue(math.isnan(math.tan(NAN)))
def testTan(self):
self.assertRaises(TypeError, math.tan)
self.ftest('tan(0)', math.tan(0), 0)
self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)
self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)
try:
self.assertTrue(math.isnan(math.tan(INF)))
self.assertTrue(math.isnan(math.tan(NINF)))
except:
self.assertRaises(ValueError, math.tan, INF)
self.assertRaises(ValueError, math.tan, NINF)
self.assertTrue(math.isnan(math.tan(NAN)))
def testSin(self):
self.assertRaises(TypeError, math.sin)
self.ftest('sin(0)', math.sin(0), 0)
self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)
self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)
try:
self.assertTrue(math.isnan(math.sin(INF)))
self.assertTrue(math.isnan(math.sin(NINF)))
except ValueError:
self.assertRaises(ValueError, math.sin, INF)
self.assertRaises(ValueError, math.sin, NINF)
self.assertTrue(math.isnan(math.sin(NAN)))
def testCos(self):
self.assertRaises(TypeError, math.cos)
self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
self.ftest('cos(0)', math.cos(0), 1)
self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
self.ftest('cos(pi)', math.cos(math.pi), -1)
try:
self.assertTrue(math.isnan(math.cos(INF)))
self.assertTrue(math.isnan(math.cos(NINF)))
except ValueError:
self.assertRaises(ValueError, math.cos, INF)
self.assertRaises(ValueError, math.cos, NINF)
self.assertTrue(math.isnan(math.cos(NAN)))
def testCos(self):
self.assertRaises(TypeError, math.cos)
self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)
self.ftest('cos(0)', math.cos(0), 1)
self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)
self.ftest('cos(pi)', math.cos(math.pi), -1)
try:
self.assertTrue(math.isnan(math.cos(INF)))
self.assertTrue(math.isnan(math.cos(NINF)))
except ValueError:
self.assertRaises(ValueError, math.cos, INF)
self.assertRaises(ValueError, math.cos, NINF)
self.assertTrue(math.isnan(math.cos(NAN)))
def testFloor(self):
self.assertRaises(TypeError, math.floor)
# These types will be int in py3k.
self.assertEqual(float, type(math.floor(1)))
self.assertEqual(float, type(math.floor(1L)))
self.assertEqual(float, type(math.floor(1.0)))
self.ftest('floor(0.5)', math.floor(0.5), 0)
self.ftest('floor(1.0)', math.floor(1.0), 1)
self.ftest('floor(1.5)', math.floor(1.5), 1)
self.ftest('floor(-0.5)', math.floor(-0.5), -1)
self.ftest('floor(-1.0)', math.floor(-1.0), -1)
self.ftest('floor(-1.5)', math.floor(-1.5), -2)
# pow() relies on floor() to check for integers
# This fails on some platforms - so check it here
self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
self.assertEqual(math.ceil(INF), INF)
self.assertEqual(math.ceil(NINF), NINF)
self.assertTrue(math.isnan(math.floor(NAN)))
class TestFloor(object):
def __float__(self):
return 42.3
class TestNoFloor(object):
pass
self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
self.assertRaises(TypeError, math.floor, TestNoFloor())
t = TestNoFloor()
t.__floor__ = lambda *args: args
self.assertRaises(TypeError, math.floor, t)
self.assertRaises(TypeError, math.floor, t, 0)
def testCosh(self):
self.assertRaises(TypeError, math.cosh)
self.ftest('cosh(0)', math.cosh(0), 1)
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
self.assertEqual(math.cosh(INF), INF)
self.assertEqual(math.cosh(NINF), INF)
self.assertTrue(math.isnan(math.cosh(NAN)))
def testCeil(self):
self.assertRaises(TypeError, math.ceil)
# These types will be int in py3k.
#self.assertEqual(float, type(math.ceil(1)))
#self.assertEqual(float, type(math.ceil(1L)))
#self.assertEqual(float, type(math.ceil(1.0)))
self.ftest('ceil(0.5)', math.ceil(0.5), 1)
self.ftest('ceil(1.0)', math.ceil(1.0), 1)
self.ftest('ceil(1.5)', math.ceil(1.5), 2)
self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
self.assertEqual(math.ceil(INF), INF)
self.assertEqual(math.ceil(NINF), NINF)
self.assertTrue(math.isnan(math.ceil(NAN)))
class TestCeil(object):
def __float__(self):
return 41.3
class TestNoCeil(object):
pass
self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
self.assertRaises(TypeError, math.ceil, TestNoCeil())
t = TestNoCeil()
t.__ceil__ = lambda *args: args
self.assertRaises(TypeError, math.ceil, t)
self.assertRaises(TypeError, math.ceil, t, 0)
def testCosh(self):
self.assertRaises(TypeError, math.cosh)
self.ftest('cosh(0)', math.cosh(0), 1)
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert
self.assertEqual(math.cosh(INF), INF)
self.assertEqual(math.cosh(NINF), INF)
self.assertTrue(math.isnan(math.cosh(NAN)))
def testFloor(self):
self.assertRaises(TypeError, math.floor)
# These types will be int in py3k.
self.assertEqual(float, type(math.floor(1)))
self.assertEqual(float, type(math.floor(1L)))
self.assertEqual(float, type(math.floor(1.0)))
self.ftest('floor(0.5)', math.floor(0.5), 0)
self.ftest('floor(1.0)', math.floor(1.0), 1)
self.ftest('floor(1.5)', math.floor(1.5), 1)
self.ftest('floor(-0.5)', math.floor(-0.5), -1)
self.ftest('floor(-1.0)', math.floor(-1.0), -1)
self.ftest('floor(-1.5)', math.floor(-1.5), -2)
# pow() relies on floor() to check for integers
# This fails on some platforms - so check it here
self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)
self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)
self.assertEqual(math.ceil(INF), INF)
self.assertEqual(math.ceil(NINF), NINF)
self.assertTrue(math.isnan(math.floor(NAN)))
class TestFloor(object):
def __float__(self):
return 42.3
class TestNoFloor(object):
pass
self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)
self.assertRaises(TypeError, math.floor, TestNoFloor())
t = TestNoFloor()
t.__floor__ = lambda *args: args
self.assertRaises(TypeError, math.floor, t)
self.assertRaises(TypeError, math.floor, t, 0)
def testCeil(self):
self.assertRaises(TypeError, math.ceil)
# These types will be int in py3k.
self.assertEquals(type(math.cf(0)), type(math.ceil(1)))
self.assertEquals(type(math.cf(0)), type(math.ceil(1L)))
self.assertEquals(type(math.cf(0)), type(math.ceil(1.0)))
#self.assertEqual(float, type(math.ceil(1)))
#self.assertEqual(float, type(math.ceil(1L)))
#self.assertEqual(float, type(math.ceil(1.0)))
self.ftest('ceil(0.5)', math.ceil(0.5), 1)
self.ftest('ceil(1.0)', math.ceil(1.0), 1)
self.ftest('ceil(1.5)', math.ceil(1.5), 2)
self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)
self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)
self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)
self.assertEqual(math.ceil(INF), INF)
self.assertEqual(math.ceil(NINF), NINF)
self.assertTrue(math.isnan(math.ceil(NAN)))
class TestCeil(object):
def __float__(self):
return 41.3
class TestNoCeil(object):
pass
self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)
self.assertRaises(TypeError, math.ceil, TestNoCeil())
t = TestNoCeil()
t.__ceil__ = lambda *args: args
self.assertRaises(TypeError, math.ceil, t)
self.assertRaises(TypeError, math.ceil, t, 0)
def testLog10(self):
self.assertRaises(TypeError, math.log10)
self.ftest('log10(0.1)', math.log10(0.1), -1)
self.ftest('log10(1)', math.log10(1), 0)
self.ftest('log10(10)', math.log10(10), 1)
self.assertEqual(math.log(INF), INF)
self.assertRaises(ValueError, math.log10, NINF)
self.assertTrue(math.isnan(math.log10(NAN)))
def testExp(self):
self.assertRaises(TypeError, math.exp)
self.ftest('exp(-1)', math.exp(-1), 1/math.e)
self.ftest('exp(0)', math.exp(0), 1)
self.ftest('exp(1)', math.exp(1), math.e)
self.assertEqual(math.exp(INF), INF)
self.assertEqual(math.exp(NINF), 0.)
self.assertTrue(math.isnan(math.exp(NAN)))
def testAsinh(self):
self.assertRaises(TypeError, math.asinh)
self.ftest('asinh(0)', math.asinh(0), 0)
self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
self.assertEqual(math.asinh(INF), INF)
self.assertEqual(math.asinh(NINF), NINF)
self.assertTrue(math.isnan(math.asinh(NAN)))
def testExp(self):
self.assertRaises(TypeError, math.exp)
self.ftest('exp(-1)', math.exp(-1), 1/math.e)
self.ftest('exp(0)', math.exp(0), 1)
self.ftest('exp(1)', math.exp(1), math.e)
self.assertEqual(math.exp(INF), INF)
self.assertEqual(math.exp(NINF), 0.)
self.assertTrue(math.isnan(math.exp(NAN)))
def testSqrt(self):
self.assertRaises(TypeError, math.sqrt)
self.ftest('sqrt(0)', math.sqrt(0), 0)
self.ftest('sqrt(1)', math.sqrt(1), 1)
self.ftest('sqrt(4)', math.sqrt(4), 2)
self.assertEqual(math.sqrt(INF), INF)
self.assertRaises(ValueError, math.sqrt, NINF)
self.assertTrue(math.isnan(math.sqrt(NAN)))
def testSinh(self):
self.assertRaises(TypeError, math.sinh)
self.ftest('sinh(0)', math.sinh(0), 0)
self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
self.assertEqual(math.sinh(INF), INF)
self.assertEqual(math.sinh(NINF), NINF)
self.assertTrue(math.isnan(math.sinh(NAN)))
def testSqrt(self):
self.assertRaises(TypeError, math.sqrt)
self.ftest('sqrt(0)', math.sqrt(0), 0)
self.ftest('sqrt(1)', math.sqrt(1), 1)
self.ftest('sqrt(4)', math.sqrt(4), 2)
self.assertEqual(math.sqrt(INF), INF)
self.assertRaises(ValueError, math.sqrt, NINF)
self.assertTrue(math.isnan(math.sqrt(NAN)))
def testAcos(self):
self.assertRaises(TypeError, math.acos)
self.ftest('acos(-1)', math.acos(-1), math.pi)
self.ftest('acos(0)', math.acos(0), math.pi/2)
self.ftest('acos(1)', math.acos(1), 0)
self.assertRaises(ValueError, math.acos, INF)
self.assertRaises(ValueError, math.acos, NINF)
self.assertTrue(math.isnan(math.acos(NAN)))
def testSinh(self):
self.assertRaises(TypeError, math.sinh)
self.ftest('sinh(0)', math.sinh(0), 0)
self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)
self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)
self.assertEqual(math.sinh(INF), INF)
self.assertEqual(math.sinh(NINF), NINF)
self.assertTrue(math.isnan(math.sinh(NAN)))
def testLog10(self):
self.assertRaises(TypeError, math.log10)
self.ftest('log10(0.1)', math.log10(0.1), -1)
self.ftest('log10(1)', math.log10(1), 0)
self.ftest('log10(10)', math.log10(10), 1)
self.assertEqual(math.log(INF), INF)
self.assertRaises(ValueError, math.log10, NINF)
self.assertTrue(math.isnan(math.log10(NAN)))
def testAcos(self):
self.assertRaises(TypeError, math.acos)
self.ftest('acos(-1)', math.acos(-1), math.pi)
self.ftest('acos(0)', math.acos(0), math.pi/2)
self.ftest('acos(1)', math.acos(1), 0)
self.assertRaises(ValueError, math.acos, INF)
self.assertRaises(ValueError, math.acos, NINF)
self.assertTrue(math.isnan(math.acos(NAN)))
def testAsin(self):
self.assertRaises(TypeError, math.asin)
self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
self.ftest('asin(0)', math.asin(0), 0)
self.ftest('asin(1)', math.asin(1), math.pi/2)
self.assertRaises(ValueError, math.asin, INF)
self.assertRaises(ValueError, math.asin, NINF)
self.assertTrue(math.isnan(math.asin(NAN)))
def testAtan(self):
self.assertRaises(TypeError, math.atan)
self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
self.ftest('atan(0)', math.atan(0), 0)
self.ftest('atan(1)', math.atan(1), math.pi/4)
self.ftest('atan(inf)', math.atan(INF), math.pi/2)
self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)
self.assertTrue(math.isnan(math.atan(NAN)))
def testAtan(self):
self.assertRaises(TypeError, math.atan)
self.ftest('atan(-1)', math.atan(-1), -math.pi/4)
self.ftest('atan(0)', math.atan(0), 0)
self.ftest('atan(1)', math.atan(1), math.pi/4)
self.ftest('atan(inf)', math.atan(INF), math.pi/2)
self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)
self.assertTrue(math.isnan(math.atan(NAN)))
def testAsin(self):
self.assertRaises(TypeError, math.asin)
self.ftest('asin(-1)', math.asin(-1), -math.pi/2)
self.ftest('asin(0)', math.asin(0), 0)
self.ftest('asin(1)', math.asin(1), math.pi/2)
self.assertRaises(ValueError, math.asin, INF)
self.assertRaises(ValueError, math.asin, NINF)
self.assertTrue(math.isnan(math.asin(NAN)))
def testAsinh(self):
self.assertRaises(TypeError, math.asinh)
self.ftest('asinh(0)', math.asinh(0), 0)
self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)
self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)
self.assertEqual(math.asinh(INF), INF)
self.assertEqual(math.asinh(NINF), NINF)
self.assertTrue(math.isnan(math.asinh(NAN)))
def testModf(self):
self.assertRaises(TypeError, math.modf)
def testmodf(name, result, expected):
(v1, v2), (e1, e2) = result, expected
if abs(v1-e1) > eps or abs(v2-e2):
self.fail('%s returned %r, expected %r'%\
(name, (v1,v2), (e1,e2)))
testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
self.assertEqual(math.modf(INF), (0.0, INF))
self.assertEqual(math.modf(NINF), (-0.0, NINF))
modf_nan = math.modf(NAN)
self.assertTrue(math.isnan(modf_nan[0]))
self.assertTrue(math.isnan(modf_nan[1]))
def testAcosh(self):
self.assertRaises(TypeError, math.acosh)
self.ftest('acosh(1)', math.acosh(1), 0)
self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
self.assertRaises(ValueError, math.acosh, 0)
self.assertRaises(ValueError, math.acosh, -1)
self.assertEqual(math.acosh(INF), INF)
self.assertRaises(ValueError, math.acosh, NINF)
self.assertTrue(math.isnan(math.acosh(NAN)))
def testModf(self):
self.assertRaises(TypeError, math.modf)
def testmodf(name, result, expected):
(v1, v2), (e1, e2) = result, expected
if abs(v1-e1) > eps or abs(v2-e2):
self.fail('%s returned %r, expected %r'%\
(name, (v1,v2), (e1,e2)))
testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))
testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))
self.assertEqual(math.modf(INF), (0.0, INF))
self.assertEqual(math.modf(NINF), (-0.0, NINF))
modf_nan = math.modf(NAN)
self.assertTrue(math.isnan(modf_nan[0]))
self.assertTrue(math.isnan(modf_nan[1]))
def testAcosh(self):
self.assertRaises(TypeError, math.acosh)
self.ftest('acosh(1)', math.acosh(1), 0)
self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)
self.assertRaises(ValueError, math.acosh, 0)
self.assertRaises(ValueError, math.acosh, -1)
self.assertEqual(math.acosh(INF), INF)
self.assertRaises(ValueError, math.acosh, NINF)
self.assertTrue(math.isnan(math.acosh(NAN)))
def testAtanh(self):
self.assertRaises(TypeError, math.atan)
self.ftest('atanh(0)', math.atanh(0), 0)
self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
self.assertRaises(ValueError, math.atanh, 1)
self.assertRaises(ValueError, math.atanh, -1)
self.assertRaises(ValueError, math.atanh, INF)
self.assertRaises(ValueError, math.atanh, NINF)
self.assertTrue(math.isnan(math.atanh(NAN)))
def testAtanh(self):
self.assertRaises(TypeError, math.atan)
self.ftest('atanh(0)', math.atanh(0), 0)
self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)
self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)
self.assertRaises(ValueError, math.atanh, 1)
self.assertRaises(ValueError, math.atanh, -1)
self.assertRaises(ValueError, math.atanh, INF)
self.assertRaises(ValueError, math.atanh, NINF)
self.assertTrue(math.isnan(math.atanh(NAN)))
def testLog(self):
self.assertRaises(TypeError, math.log)
self.ftest('log(1/e)', math.log(1/math.e), -1)
self.ftest('log(1)', math.log(1), 0)
self.ftest('log(e)', math.log(math.e), 1)
self.ftest('log(32,2)', math.log(32,2), 5)
self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
self.assertEqual(math.log(INF), INF)
self.assertRaises(ValueError, math.log, NINF)
self.assertTrue(math.isnan(math.log(NAN)))
def testLog(self):
self.assertRaises(TypeError, math.log)
self.ftest('log(1/e)', math.log(1/math.e), -1)
self.ftest('log(1)', math.log(1), 0)
self.ftest('log(e)', math.log(math.e), 1)
self.ftest('log(32,2)', math.log(32,2), 5)
self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)
self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)
self.assertEqual(math.log(INF), INF)
self.assertRaises(ValueError, math.log, NINF)
self.assertTrue(math.isnan(math.log(NAN)))
def testFmod(self):
self.assertRaises(TypeError, math.fmod)
self.ftest('fmod(10,1)', math.fmod(10,1), 0)
self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0)
self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1)
self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)
self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)
self.assertTrue(math.isnan(math.fmod(NAN, 1.)))
self.assertTrue(math.isnan(math.fmod(1., NAN)))
self.assertTrue(math.isnan(math.fmod(NAN, NAN)))
self.assertRaises(ValueError, math.fmod, 1., 0.)
self.assertRaises(ValueError, math.fmod, INF, 1.)
self.assertRaises(ValueError, math.fmod, NINF, 1.)
self.assertRaises(ValueError, math.fmod, INF, 0.)
self.assertEqual(math.fmod(3.0, INF), 3.0)
self.assertEqual(math.fmod(-3.0, INF), -3.0)
self.assertEqual(math.fmod(3.0, NINF), 3.0)
self.assertEqual(math.fmod(-3.0, NINF), -3.0)
self.assertEqual(math.fmod(0.0, 3.0), 0.0)
self.assertEqual(math.fmod(0.0, NINF), 0.0)
def testTanh(self):
self.assertRaises(TypeError, math.tanh)
self.ftest('tanh(0)', math.tanh(0), 0)
self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
self.ftest('tanh(inf)', math.tanh(INF), 1)
self.ftest('tanh(-inf)', math.tanh(NINF), -1)
self.assertTrue(math.isnan(math.tanh(NAN)))
# check that tanh(-0.) == -0. on IEEE 754 systems
if float.__getformat__("double").startswith("IEEE"):
self.assertEqual(math.tanh(-0.), -0.)
self.assertEqual(math.copysign(1., math.tanh(-0.)),
math.copysign(1., -0.))
def testLog1p(self):
self.assertRaises(TypeError, math.log1p)
self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1)
self.ftest('log1p(0)', math.log1p(0), 0)
self.ftest('log1p(e-1)', math.log1p(math.e-1), 1)
self.ftest('log1p(1)', math.log1p(1), math.log(2))
self.assertEqual(math.log1p(INF), INF)
self.assertRaises(ValueError, math.log1p, NINF)
self.assertTrue(math.isnan(math.log1p(NAN)))
n= 2**90
self.assertAlmostEqual(math.log1p(n), 62.383246250395075)
self.assertAlmostEqual(math.log1p(n), math.log1p(float(n)))
def testLog1p(self):
self.assertRaises(TypeError, math.log1p)
self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1)
self.ftest('log1p(0)', math.log1p(0), 0)
self.ftest('log1p(e-1)', math.log1p(math.e-1), 1)
self.ftest('log1p(1)', math.log1p(1), math.log(2))
self.assertEqual(math.log1p(INF), INF)
self.assertRaises(ValueError, math.log1p, NINF)
self.assertTrue(math.isnan(math.log1p(NAN)))
n= 2**90
self.assertAlmostEqual(math.log1p(n), 62.383246250395075)
self.assertAlmostEqual(math.log1p(n), math.log1p(float(n)))
def testTanh(self):
self.assertRaises(TypeError, math.tanh)
self.ftest('tanh(0)', math.tanh(0), 0)
self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)
self.ftest('tanh(inf)', math.tanh(INF), 1)
self.ftest('tanh(-inf)', math.tanh(NINF), -1)
self.assertTrue(math.isnan(math.tanh(NAN)))
# check that tanh(-0.) == -0. on IEEE 754 systems
if float.__getformat__("double").startswith("IEEE"):
self.assertEqual(math.tanh(-0.), -0.)
self.assertEqual(math.copysign(1., math.tanh(-0.)),
math.copysign(1., -0.))
def testFmod(self):
self.assertRaises(TypeError, math.fmod)
self.ftest('fmod(10,1)', math.fmod(10,1), 0)
self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0)
self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1)
self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)
self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)
self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)
self.assertTrue(math.isnan(math.fmod(NAN, 1.)))
self.assertTrue(math.isnan(math.fmod(1., NAN)))
self.assertTrue(math.isnan(math.fmod(NAN, NAN)))
self.assertRaises(ValueError, math.fmod, 1., 0.)
self.assertRaises(ValueError, math.fmod, INF, 1.)
self.assertRaises(ValueError, math.fmod, NINF, 1.)
self.assertRaises(ValueError, math.fmod, INF, 0.)
self.assertEqual(math.fmod(3.0, INF), 3.0)
self.assertEqual(math.fmod(-3.0, INF), -3.0)
self.assertEqual(math.fmod(3.0, NINF), 3.0)
self.assertEqual(math.fmod(-3.0, NINF), -3.0)
self.assertEqual(math.fmod(0.0, 3.0), 0.0)
self.assertEqual(math.fmod(0.0, NINF), 0.0)
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)
#self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
#self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
self.assertTrue(math.ldexp(1.0,100000)>0)
self.assertTrue(math.ldexp(-1.0,100000)<0)
#cf don't return +-0 for big numbers in ldexp function
#self.assertEquals(math.ldexp(1., -1000000), 0.)
#self.assertEquals(math.ldexp(-1., -1000000), -0.)
self.assertEquals(math.ldexp(INF, 30), INF)
self.assertEquals(math.ldexp(NINF, -213), NINF)
self.assert_(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEquals(math.ldexp(INF, -n), INF)
self.assertEquals(math.ldexp(NINF, -n), NINF)
#cf doesn't return 0/-0
#self.assertEquals(math.ldexp(1., -n), 0.)
#self.assertEquals(math.ldexp(-1., -n), -0.)
self.assertEquals(math.ldexp(0., -n), 0.)
self.assertEquals(math.ldexp(-0., -n), -0.)
self.assert_(math.isnan(math.ldexp(NAN, -n)))
#cf doesn't raise exceptions
#self.assertRaises(OverflowError, math.ldexp, 1., n)
#self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEquals(math.ldexp(0., n), 0.)
self.assertEquals(math.ldexp(-0., n), -0.)
self.assertEquals(math.ldexp(INF, n), INF)
self.assertEquals(math.ldexp(NINF, n), NINF)
self.assert_(math.isnan(math.ldexp(NAN, n)))
def testLdexp(self):
self.assertRaises(TypeError, math.ldexp)
self.ftest('ldexp(0,1)', math.ldexp(0, 1), 0)
self.ftest('ldexp(1,1)', math.ldexp(1, 1), 2)
self.ftest('ldexp(1,-1)', math.ldexp(1, -1), 0.5)
self.ftest('ldexp(-1,1)', math.ldexp(-1, 1), -2)
#self.assertRaises(OverflowError, math.ldexp, 1., 1000000)
#self.assertRaises(OverflowError, math.ldexp, -1., 1000000)
self.assertTrue(math.ldexp(1.0, 100000) > 0)
self.assertTrue(math.ldexp(-1.0, 100000) < 0)
#cf don't return +-0 for big numbers in ldexp function
#self.assertEquals(math.ldexp(1., -1000000), 0.)
#self.assertEquals(math.ldexp(-1., -1000000), -0.)
self.assertEquals(math.ldexp(INF, 30), INF)
self.assertEquals(math.ldexp(NINF, -213), NINF)
self.assert_(math.isnan(math.ldexp(NAN, 0)))
# large second argument
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:
self.assertEquals(math.ldexp(INF, -n), INF)
self.assertEquals(math.ldexp(NINF, -n), NINF)
#cf doesn't return 0/-0
#self.assertEquals(math.ldexp(1., -n), 0.)
#self.assertEquals(math.ldexp(-1., -n), -0.)
self.assertEquals(math.ldexp(0., -n), 0.)
self.assertEquals(math.ldexp(-0., -n), -0.)
self.assert_(math.isnan(math.ldexp(NAN, -n)))
#cf doesn't raise exceptions
#self.assertRaises(OverflowError, math.ldexp, 1., n)
#self.assertRaises(OverflowError, math.ldexp, -1., n)
self.assertEquals(math.ldexp(0., n), 0.)
self.assertEquals(math.ldexp(-0., n), -0.)
self.assertEquals(math.ldexp(INF, n), INF)
self.assertEquals(math.ldexp(NINF, n), NINF)
self.assert_(math.isnan(math.ldexp(NAN, n)))
def testFrexp(self):
self.assertRaises(TypeError, math.frexp)
def testfrexp(name, result, expected):
(mant, exp), (emant, eexp) = result, expected
if abs(mant-emant) > eps or exp != eexp:
self.fail('%s returned %r, expected %r'%\
(name, (mant, exp), (emant,eexp)))
testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
testfrexp('frexp(0)', math.frexp(0), (0, 0))
testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
self.assertEqual(math.frexp(INF)[0], INF)
self.assertEqual(math.frexp(NINF)[0], NINF)
self.assertTrue(math.isnan(math.frexp(NAN)[0]))
def testFrexp(self):
self.assertRaises(TypeError, math.frexp)
def testfrexp(name, result, expected):
(mant, exp), (emant, eexp) = result, expected
if abs(mant-emant) > eps or exp != eexp:
self.fail('%s returned %r, expected %r'%\
(name, (mant, exp), (emant,eexp)))
testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))
testfrexp('frexp(0)', math.frexp(0), (0, 0))
testfrexp('frexp(1)', math.frexp(1), (0.5, 1))
testfrexp('frexp(2)', math.frexp(2), (0.5, 2))
self.assertEqual(math.frexp(INF)[0], INF)
self.assertEqual(math.frexp(NINF)[0], NINF)
self.assertTrue(math.isnan(math.frexp(NAN)[0]))
def testPow(self):
self.assertRaises(TypeError, math.pow)
self.ftest('pow(0,1)', math.pow(0,1), 0)
self.ftest('pow(1,0)', math.pow(1,0), 1)
self.ftest('pow(2,1)', math.pow(2,1), 2)
self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
self.assertEqual(math.pow(INF, 1), INF)
self.assertEqual(math.pow(NINF, 1), NINF)
self.assertEqual((math.pow(1, INF)), 1.)
self.assertEqual((math.pow(1, NINF)), 1.)
self.assertTrue(math.isnan(math.pow(NAN, 1)))
self.assertTrue(math.isnan(math.pow(2, NAN)))
self.assertTrue(math.isnan(math.pow(0, NAN)))
self.assertEqual(math.pow(1, NAN), 1)
# pow(0., x)
self.assertEqual(math.pow(0., INF), 0.)
self.assertEqual(math.pow(0., 3.), 0.)
self.assertEqual(math.pow(0., 2.3), 0.)
self.assertEqual(math.pow(0., 2.), 0.)
self.assertEqual(math.pow(0., 0.), 1.)
self.assertEqual(math.pow(0., -0.), 1.)
self.assertRaises(ValueError, math.pow, 0., -2.)
self.assertRaises(ValueError, math.pow, 0., -2.3)
self.assertRaises(ValueError, math.pow, 0., -3.)
self.assertRaises(ValueError, math.pow, 0., NINF)
self.assertTrue(math.isnan(math.pow(0., NAN)))
# pow(INF, x)
self.assertEqual(math.pow(INF, INF), INF)
self.assertEqual(math.pow(INF, 3.), INF)
self.assertEqual(math.pow(INF, 2.3), INF)
self.assertEqual(math.pow(INF, 2.), INF)
self.assertEqual(math.pow(INF, 0.), 1.)
self.assertEqual(math.pow(INF, -0.), 1.)
self.assertEqual(math.pow(INF, -2.), 0.)
self.assertEqual(math.pow(INF, -2.3), 0.)
self.assertEqual(math.pow(INF, -3.), 0.)
self.assertEqual(math.pow(INF, NINF), 0.)
self.assertTrue(math.isnan(math.pow(INF, NAN)))
# pow(-0., x)
self.assertEqual(math.pow(-0., INF), 0.)
self.assertEqual(math.pow(-0., 3.), -0.)
self.assertEqual(math.pow(-0., 2.3), 0.)
self.assertEqual(math.pow(-0., 2.), 0.)
self.assertEqual(math.pow(-0., 0.), 1.)
self.assertEqual(math.pow(-0., -0.), 1.)
self.assertRaises(ValueError, math.pow, -0., -2.)
self.assertRaises(ValueError, math.pow, -0., -2.3)
self.assertRaises(ValueError, math.pow, -0., -3.)
self.assertRaises(ValueError, math.pow, -0., NINF)
self.assertTrue(math.isnan(math.pow(-0., NAN)))
# pow(NINF, x)
self.assertEqual(math.pow(NINF, INF), INF)
self.assertEqual(math.pow(NINF, 3.), NINF)
self.assertEqual(math.pow(NINF, 2.3), INF)
self.assertEqual(math.pow(NINF, 2.), INF)
self.assertEqual(math.pow(NINF, 0.), 1.)
self.assertEqual(math.pow(NINF, -0.), 1.)
self.assertEqual(math.pow(NINF, -2.), 0.)
self.assertEqual(math.pow(NINF, -2.3), 0.)
self.assertEqual(math.pow(NINF, -3.), -0.)
self.assertEqual(math.pow(NINF, NINF), 0.)
self.assertTrue(math.isnan(math.pow(NINF, NAN)))
# pow(-1, x)
self.assertEqual(math.pow(-1., INF), 1.)
self.assertEqual(math.pow(-1., 3.), -1.)
self.assertRaises(ValueError, math.pow, -1., 2.3)
self.assertEqual(math.pow(-1., 2.), 1.)
self.assertEqual(math.pow(-1., 0.), 1.)
self.assertEqual(math.pow(-1., -0.), 1.)
self.assertEqual(math.pow(-1., -2.), 1.)
self.assertRaises(ValueError, math.pow, -1., -2.3)
self.assertEqual(math.pow(-1., -3.), -1.)
self.assertEqual(math.pow(-1., NINF), 1.)
self.assertTrue(math.isnan(math.pow(-1., NAN)))
# pow(1, x)
self.assertEqual(math.pow(1., INF), 1.)
self.assertEqual(math.pow(1., 3.), 1.)
self.assertEqual(math.pow(1., 2.3), 1.)
self.assertEqual(math.pow(1., 2.), 1.)
self.assertEqual(math.pow(1., 0.), 1.)
self.assertEqual(math.pow(1., -0.), 1.)
self.assertEqual(math.pow(1., -2.), 1.)
self.assertEqual(math.pow(1., -2.3), 1.)
self.assertEqual(math.pow(1., -3.), 1.)
self.assertEqual(math.pow(1., NINF), 1.)
self.assertEqual(math.pow(1., NAN), 1.)
# pow(x, 0) should be 1 for any x
self.assertEqual(math.pow(2.3, 0.), 1.)
self.assertEqual(math.pow(-2.3, 0.), 1.)
self.assertEqual(math.pow(NAN, 0.), 1.)
self.assertEqual(math.pow(2.3, -0.), 1.)
self.assertEqual(math.pow(-2.3, -0.), 1.)
self.assertEqual(math.pow(NAN, -0.), 1.)
# pow(x, y) is invalid if x is negative and y is not integral
self.assertRaises(ValueError, math.pow, -1., 2.3)
self.assertRaises(ValueError, math.pow, -15., -3.1)
# pow(x, NINF)
self.assertEqual(math.pow(1.9, NINF), 0.)
self.assertEqual(math.pow(1.1, NINF), 0.)
self.assertEqual(math.pow(0.9, NINF), INF)
self.assertEqual(math.pow(0.1, NINF), INF)
self.assertEqual(math.pow(-0.1, NINF), INF)
self.assertEqual(math.pow(-0.9, NINF), INF)
self.assertEqual(math.pow(-1.1, NINF), 0.)
self.assertEqual(math.pow(-1.9, NINF), 0.)
# pow(x, INF)
self.assertEqual(math.pow(1.9, INF), INF)
self.assertEqual(math.pow(1.1, INF), INF)
self.assertEqual(math.pow(0.9, INF), 0.)
self.assertEqual(math.pow(0.1, INF), 0.)
self.assertEqual(math.pow(-0.1, INF), 0.)
self.assertEqual(math.pow(-0.9, INF), 0.)
self.assertEqual(math.pow(-1.1, INF), INF)
self.assertEqual(math.pow(-1.9, INF), INF)
# pow(x, y) should work for x negative, y an integer
self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)
self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)
self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)
self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)
self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)
self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)
self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)
self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)
self.assertRaises(ValueError, math.pow, -2.0, -0.5)
self.assertRaises(ValueError, math.pow, -2.0, 0.5)
def testIsnan(self):
self.assertTrue(math.isnan(float("nan")))
self.assertTrue(math.isnan(float("inf")* 0.))
self.assertFalse(math.isnan(float("inf")))
self.assertFalse(math.isnan(0.))
self.assertFalse(math.isnan(1.))
def testAtan2(self):
self.assertRaises(TypeError, math.atan2)
self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)
# math.atan2(0, x)
self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)
self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)
self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)
self.assertEqual(math.atan2(0., 0.), 0.)
self.assertEqual(math.atan2(0., 2.3), 0.)
self.assertEqual(math.atan2(0., INF), 0.)
self.assertTrue(math.isnan(math.atan2(0., NAN)))
# math.atan2(-0, x)
self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)
self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)
self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)
self.assertEqual(math.atan2(-0., 0.), -0.)
self.assertEqual(math.atan2(-0., 2.3), -0.)
self.assertEqual(math.atan2(-0., INF), -0.)
self.assertTrue(math.isnan(math.atan2(-0., NAN)))
# math.atan2(INF, x)
self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)
self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)
self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)
self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)
self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)
self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)
self.assertTrue(math.isnan(math.atan2(INF, NAN)))
# math.atan2(NINF, x)
self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)
self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)
self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)
self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)
self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)
self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)
self.assertTrue(math.isnan(math.atan2(NINF, NAN)))
# math.atan2(+finite, x)
self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)
self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)
self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)
self.assertEqual(math.atan2(2.3, INF), 0.)
self.assertTrue(math.isnan(math.atan2(2.3, NAN)))
# math.atan2(-finite, x)
self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)
self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)
self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)
self.assertEqual(math.atan2(-2.3, INF), -0.)
self.assertTrue(math.isnan(math.atan2(-2.3, NAN)))
# math.atan2(NAN, x)
self.assertTrue(math.isnan(math.atan2(NAN, NINF)))
self.assertTrue(math.isnan(math.atan2(NAN, -2.3)))
self.assertTrue(math.isnan(math.atan2(NAN, -0.)))
self.assertTrue(math.isnan(math.atan2(NAN, 0.)))
self.assertTrue(math.isnan(math.atan2(NAN, 2.3)))
self.assertTrue(math.isnan(math.atan2(NAN, INF)))
self.assertTrue(math.isnan(math.atan2(NAN, NAN)))
def testPow(self):
self.assertRaises(TypeError, math.pow)
self.ftest('pow(0,1)', math.pow(0,1), 0)
self.ftest('pow(1,0)', math.pow(1,0), 1)
self.ftest('pow(2,1)', math.pow(2,1), 2)
self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)
self.assertEqual(math.pow(INF, 1), INF)
self.assertEqual(math.pow(NINF, 1), NINF)
self.assertEqual((math.pow(1, INF)), 1.)
self.assertEqual((math.pow(1, NINF)), 1.)
self.assertTrue(math.isnan(math.pow(NAN, 1)))
self.assertTrue(math.isnan(math.pow(2, NAN)))
self.assertTrue(math.isnan(math.pow(0, NAN)))
self.assertEqual(math.pow(1, NAN), 1)
# pow(0., x)
self.assertEqual(math.pow(0., INF), 0.)
self.assertEqual(math.pow(0., 3.), 0.)
self.assertEqual(math.pow(0., 2.3), 0.)
self.assertEqual(math.pow(0., 2.), 0.)
self.assertEqual(math.pow(0., 0.), 1.)
self.assertEqual(math.pow(0., -0.), 1.)
self.assertRaises(ValueError, math.pow, 0., -2.)
self.assertRaises(ValueError, math.pow, 0., -2.3)
self.assertRaises(ValueError, math.pow, 0., -3.)
self.assertRaises(ValueError, math.pow, 0., NINF)
self.assertTrue(math.isnan(math.pow(0., NAN)))
# pow(INF, x)
self.assertEqual(math.pow(INF, INF), INF)
self.assertEqual(math.pow(INF, 3.), INF)
self.assertEqual(math.pow(INF, 2.3), INF)
self.assertEqual(math.pow(INF, 2.), INF)
self.assertEqual(math.pow(INF, 0.), 1.)
self.assertEqual(math.pow(INF, -0.), 1.)
self.assertEqual(math.pow(INF, -2.), 0.)
self.assertEqual(math.pow(INF, -2.3), 0.)
self.assertEqual(math.pow(INF, -3.), 0.)
self.assertEqual(math.pow(INF, NINF), 0.)
self.assertTrue(math.isnan(math.pow(INF, NAN)))
# pow(-0., x)
self.assertEqual(math.pow(-0., INF), 0.)
self.assertEqual(math.pow(-0., 3.), -0.)
self.assertEqual(math.pow(-0., 2.3), 0.)
self.assertEqual(math.pow(-0., 2.), 0.)
self.assertEqual(math.pow(-0., 0.), 1.)
self.assertEqual(math.pow(-0., -0.), 1.)
self.assertRaises(ValueError, math.pow, -0., -2.)
self.assertRaises(ValueError, math.pow, -0., -2.3)
self.assertRaises(ValueError, math.pow, -0., -3.)
self.assertRaises(ValueError, math.pow, -0., NINF)
self.assertTrue(math.isnan(math.pow(-0., NAN)))
# pow(NINF, x)
self.assertEqual(math.pow(NINF, INF), INF)
self.assertEqual(math.pow(NINF, 3.), NINF)
self.assertEqual(math.pow(NINF, 2.3), INF)
self.assertEqual(math.pow(NINF, 2.), INF)
self.assertEqual(math.pow(NINF, 0.), 1.)
self.assertEqual(math.pow(NINF, -0.), 1.)
self.assertEqual(math.pow(NINF, -2.), 0.)
self.assertEqual(math.pow(NINF, -2.3), 0.)
self.assertEqual(math.pow(NINF, -3.), -0.)
self.assertEqual(math.pow(NINF, NINF), 0.)
self.assertTrue(math.isnan(math.pow(NINF, NAN)))
# pow(-1, x)
self.assertEqual(math.pow(-1., INF), 1.)
self.assertEqual(math.pow(-1., 3.), -1.)
self.assertRaises(ValueError, math.pow, -1., 2.3)
self.assertEqual(math.pow(-1., 2.), 1.)
self.assertEqual(math.pow(-1., 0.), 1.)
self.assertEqual(math.pow(-1., -0.), 1.)
self.assertEqual(math.pow(-1., -2.), 1.)
self.assertRaises(ValueError, math.pow, -1., -2.3)
self.assertEqual(math.pow(-1., -3.), -1.)
self.assertEqual(math.pow(-1., NINF), 1.)
self.assertTrue(math.isnan(math.pow(-1., NAN)))
# pow(1, x)
self.assertEqual(math.pow(1., INF), 1.)
self.assertEqual(math.pow(1., 3.), 1.)
self.assertEqual(math.pow(1., 2.3), 1.)
self.assertEqual(math.pow(1., 2.), 1.)
self.assertEqual(math.pow(1., 0.), 1.)
self.assertEqual(math.pow(1., -0.), 1.)
self.assertEqual(math.pow(1., -2.), 1.)
self.assertEqual(math.pow(1., -2.3), 1.)
self.assertEqual(math.pow(1., -3.), 1.)
self.assertEqual(math.pow(1., NINF), 1.)
self.assertEqual(math.pow(1., NAN), 1.)
# pow(x, 0) should be 1 for any x
self.assertEqual(math.pow(2.3, 0.), 1.)
self.assertEqual(math.pow(-2.3, 0.), 1.)
self.assertEqual(math.pow(NAN, 0.), 1.)
self.assertEqual(math.pow(2.3, -0.), 1.)
self.assertEqual(math.pow(-2.3, -0.), 1.)
self.assertEqual(math.pow(NAN, -0.), 1.)
# pow(x, y) is invalid if x is negative and y is not integral
self.assertRaises(ValueError, math.pow, -1., 2.3)
self.assertRaises(ValueError, math.pow, -15., -3.1)
# pow(x, NINF)
self.assertEqual(math.pow(1.9, NINF), 0.)
self.assertEqual(math.pow(1.1, NINF), 0.)
self.assertEqual(math.pow(0.9, NINF), INF)
self.assertEqual(math.pow(0.1, NINF), INF)
self.assertEqual(math.pow(-0.1, NINF), INF)
self.assertEqual(math.pow(-0.9, NINF), INF)
self.assertEqual(math.pow(-1.1, NINF), 0.)
self.assertEqual(math.pow(-1.9, NINF), 0.)
# pow(x, INF)
self.assertEqual(math.pow(1.9, INF), INF)
self.assertEqual(math.pow(1.1, INF), INF)
self.assertEqual(math.pow(0.9, INF), 0.)
self.assertEqual(math.pow(0.1, INF), 0.)
self.assertEqual(math.pow(-0.1, INF), 0.)
self.assertEqual(math.pow(-0.9, INF), 0.)
self.assertEqual(math.pow(-1.1, INF), INF)
self.assertEqual(math.pow(-1.9, INF), INF)
# pow(x, y) should work for x negative, y an integer
self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)
self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)
self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)
self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)
self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)
self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)
self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)
self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)
self.assertRaises(ValueError, math.pow, -2.0, -0.5)
self.assertRaises(ValueError, math.pow, -2.0, 0.5)
def testIsnan(self):
self.assertTrue(math.isnan(float("nan")))
self.assertTrue(math.isnan(float("inf")* 0.))
self.assertFalse(math.isnan(float("inf")))
self.assertFalse(math.isnan(0.))
self.assertFalse(math.isnan(1.))
def testAtan2(self):
self.assertRaises(TypeError, math.atan2)
self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)
self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)
self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)
self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)
self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)
# math.atan2(0, x)
self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)
self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)
self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)
self.assertEqual(math.atan2(0., 0.), 0.)
self.assertEqual(math.atan2(0., 2.3), 0.)
self.assertEqual(math.atan2(0., INF), 0.)
self.assertTrue(math.isnan(math.atan2(0., NAN)))
# math.atan2(-0, x)
self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)
self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)
self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)
self.assertEqual(math.atan2(-0., 0.), -0.)
self.assertEqual(math.atan2(-0., 2.3), -0.)
self.assertEqual(math.atan2(-0., INF), -0.)
self.assertTrue(math.isnan(math.atan2(-0., NAN)))
# math.atan2(INF, x)
self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)
self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)
self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)
self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)
self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)
self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)
self.assertTrue(math.isnan(math.atan2(INF, NAN)))
# math.atan2(NINF, x)
self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)
self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)
self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)
self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)
self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)
self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)
self.assertTrue(math.isnan(math.atan2(NINF, NAN)))
# math.atan2(+finite, x)
self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)
self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)
self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)
self.assertEqual(math.atan2(2.3, INF), 0.)
self.assertTrue(math.isnan(math.atan2(2.3, NAN)))
# math.atan2(-finite, x)
self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)
self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)
self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)
self.assertEqual(math.atan2(-2.3, INF), -0.)
self.assertTrue(math.isnan(math.atan2(-2.3, NAN)))
# math.atan2(NAN, x)
self.assertTrue(math.isnan(math.atan2(NAN, NINF)))
self.assertTrue(math.isnan(math.atan2(NAN, -2.3)))
self.assertTrue(math.isnan(math.atan2(NAN, -0.)))
self.assertTrue(math.isnan(math.atan2(NAN, 0.)))
self.assertTrue(math.isnan(math.atan2(NAN, 2.3)))
self.assertTrue(math.isnan(math.atan2(NAN, INF)))
self.assertTrue(math.isnan(math.atan2(NAN, NAN)))
