--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/symbian-qemu-0.9.1-12/python-2.6.1/Lib/test/test_math.py Fri Jul 31 15:01:17 2009 +0100
@@ -0,0 +1,894 @@
+# Python test set -- math module
+# XXXX Should not do tests around zero only
+
+from test.test_support import run_unittest, verbose
+import unittest
+import math
+import os
+import sys
+import random
+
+eps = 1E-05
+NAN = float('nan')
+INF = float('inf')
+NINF = float('-inf')
+
+# locate file with test values
+if __name__ == '__main__':
+ file = sys.argv[0]
+else:
+ file = __file__
+test_dir = os.path.dirname(file) or os.curdir
+test_file = os.path.join(test_dir, 'cmath_testcases.txt')
+
+def parse_testfile(fname):
+ """Parse a file with test values
+
+ Empty lines or lines starting with -- are ignored
+ yields id, fn, arg_real, arg_imag, exp_real, exp_imag
+ """
+ with open(fname) as fp:
+ for line in fp:
+ # skip comment lines and blank lines
+ if line.startswith('--') or not line.strip():
+ continue
+
+ lhs, rhs = line.split('->')
+ id, fn, arg_real, arg_imag = lhs.split()
+ rhs_pieces = rhs.split()
+ exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]
+ flags = rhs_pieces[2:]
+
+ yield (id, fn,
+ float(arg_real), float(arg_imag),
+ float(exp_real), float(exp_imag),
+ flags
+ )
+
+class MathTests(unittest.TestCase):
+
+ def ftest(self, name, value, expected):
+ if abs(value-expected) > eps:
+ # Use %r instead of %f so the error message
+ # displays full precision. Otherwise discrepancies
+ # in the last few bits will lead to very confusing
+ # error messages
+ self.fail('%s returned %r, expected %r' %
+ (name, value, expected))
+
+ def testConstants(self):
+ self.ftest('pi', math.pi, 3.1415926)
+ self.ftest('e', math.e, 2.7182818)
+
+ 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.assert_(math.isnan(math.acos(NAN)))
+
+ 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.assertEquals(math.acosh(INF), INF)
+ self.assertRaises(ValueError, math.acosh, NINF)
+ self.assert_(math.isnan(math.acosh(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.assert_(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.assertEquals(math.asinh(INF), INF)
+ self.assertEquals(math.asinh(NINF), NINF)
+ self.assert_(math.isnan(math.asinh(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.assert_(math.isnan(math.atan(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.assert_(math.isnan(math.atanh(NAN)))
+
+ 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.assert_(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.assert_(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.assert_(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.assert_(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.assert_(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.assert_(math.isnan(math.atan2(-2.3, NAN)))
+ # math.atan2(NAN, x)
+ self.assert_(math.isnan(math.atan2(NAN, NINF)))
+ self.assert_(math.isnan(math.atan2(NAN, -2.3)))
+ self.assert_(math.isnan(math.atan2(NAN, -0.)))
+ self.assert_(math.isnan(math.atan2(NAN, 0.)))
+ self.assert_(math.isnan(math.atan2(NAN, 2.3)))
+ self.assert_(math.isnan(math.atan2(NAN, INF)))
+ self.assert_(math.isnan(math.atan2(NAN, NAN)))
+
+ def testCeil(self):
+ self.assertRaises(TypeError, math.ceil)
+ # These types will be int in py3k.
+ self.assertEquals(float, type(math.ceil(1)))
+ self.assertEquals(float, type(math.ceil(1L)))
+ self.assertEquals(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.assertEquals(math.ceil(INF), INF)
+ self.assertEquals(math.ceil(NINF), NINF)
+ self.assert_(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)
+
+ if float.__getformat__("double").startswith("IEEE"):
+ def testCopysign(self):
+ self.assertRaises(TypeError, math.copysign)
+ # copysign should let us distinguish signs of zeros
+ self.assertEquals(copysign(1., 0.), 1.)
+ self.assertEquals(copysign(1., -0.), -1.)
+ self.assertEquals(copysign(INF, 0.), INF)
+ self.assertEquals(copysign(INF, -0.), NINF)
+ self.assertEquals(copysign(NINF, 0.), INF)
+ self.assertEquals(copysign(NINF, -0.), NINF)
+ # and of infinities
+ self.assertEquals(copysign(1., INF), 1.)
+ self.assertEquals(copysign(1., NINF), -1.)
+ self.assertEquals(copysign(INF, INF), INF)
+ self.assertEquals(copysign(INF, NINF), NINF)
+ self.assertEquals(copysign(NINF, INF), INF)
+ self.assertEquals(copysign(NINF, NINF), NINF)
+ self.assert_(math.isnan(copysign(NAN, 1.)))
+ self.assert_(math.isnan(copysign(NAN, INF)))
+ self.assert_(math.isnan(copysign(NAN, NINF)))
+ self.assert_(math.isnan(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.assert_(math.isinf(copysign(INF, NAN)))
+ # similarly, copysign(2., NAN) could be 2. or -2.
+ self.assertEquals(abs(copysign(2., NAN)), 2.)
+
+ 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.assert_(math.isnan(math.cos(INF)))
+ self.assert_(math.isnan(math.cos(NINF)))
+ except ValueError:
+ self.assertRaises(ValueError, math.cos, INF)
+ self.assertRaises(ValueError, math.cos, NINF)
+ self.assert_(math.isnan(math.cos(NAN)))
+
+ 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.assertEquals(math.cosh(INF), INF)
+ self.assertEquals(math.cosh(NINF), INF)
+ self.assert_(math.isnan(math.cosh(NAN)))
+
+ def testDegrees(self):
+ self.assertRaises(TypeError, math.degrees)
+ self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)
+ self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)
+ self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)
+
+ 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.assertEquals(math.exp(INF), INF)
+ self.assertEquals(math.exp(NINF), 0.)
+ self.assert_(math.isnan(math.exp(NAN)))
+
+ def testFabs(self):
+ self.assertRaises(TypeError, math.fabs)
+ self.ftest('fabs(-1)', math.fabs(-1), 1)
+ self.ftest('fabs(0)', math.fabs(0), 0)
+ self.ftest('fabs(1)', math.fabs(1), 1)
+
+ def testFactorial(self):
+ def fact(n):
+ result = 1
+ for i in range(1, int(n)+1):
+ result *= i
+ return result
+ values = range(10) + [50, 100, 500]
+ random.shuffle(values)
+ for x in range(10):
+ for cast in (int, long, float):
+ self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x)))
+ self.assertRaises(ValueError, math.factorial, -1)
+ self.assertRaises(ValueError, math.factorial, math.pi)
+
+ def testFloor(self):
+ self.assertRaises(TypeError, math.floor)
+ # These types will be int in py3k.
+ self.assertEquals(float, type(math.floor(1)))
+ self.assertEquals(float, type(math.floor(1L)))
+ self.assertEquals(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.assertEquals(math.ceil(INF), INF)
+ self.assertEquals(math.ceil(NINF), NINF)
+ self.assert_(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 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.assert_(math.isnan(math.fmod(NAN, 1.)))
+ self.assert_(math.isnan(math.fmod(1., NAN)))
+ self.assert_(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.assertEquals(math.fmod(3.0, INF), 3.0)
+ self.assertEquals(math.fmod(-3.0, INF), -3.0)
+ self.assertEquals(math.fmod(3.0, NINF), 3.0)
+ self.assertEquals(math.fmod(-3.0, NINF), -3.0)
+ self.assertEquals(math.fmod(0.0, 3.0), 0.0)
+ self.assertEquals(math.fmod(0.0, NINF), 0.0)
+
+ def testFrexp(self):
+ self.assertRaises(TypeError, math.frexp)
+
+ def testfrexp(name, (mant, exp), (emant, eexp)):
+ 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.assertEquals(math.frexp(INF)[0], INF)
+ self.assertEquals(math.frexp(NINF)[0], NINF)
+ self.assert_(math.isnan(math.frexp(NAN)[0]))
+
+ def testFsum(self):
+ # math.fsum relies on exact rounding for correct operation.
+ # There's a known problem with IA32 floating-point that causes
+ # inexact rounding in some situations, and will cause the
+ # math.fsum tests below to fail; see issue #2937. On non IEEE
+ # 754 platforms, and on IEEE 754 platforms that exhibit the
+ # problem described in issue #2937, we simply skip the whole
+ # test.
+
+ if not float.__getformat__("double").startswith("IEEE"):
+ return
+
+ # on IEEE 754 compliant machines, both of the expressions
+ # below should round to 10000000000000002.0.
+ if 1e16+2.0 != 1e16+2.9999:
+ return
+
+ # Python version of math.fsum, for comparison. Uses a
+ # different algorithm based on frexp, ldexp and integer
+ # arithmetic.
+ from sys import float_info
+ mant_dig = float_info.mant_dig
+ etiny = float_info.min_exp - mant_dig
+
+ def msum(iterable):
+ """Full precision summation. Compute sum(iterable) without any
+ intermediate accumulation of error. Based on the 'lsum' function
+ at http://code.activestate.com/recipes/393090/
+
+ """
+ tmant, texp = 0, 0
+ for x in iterable:
+ mant, exp = math.frexp(x)
+ mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
+ if texp > exp:
+ tmant <<= texp-exp
+ texp = exp
+ else:
+ mant <<= exp-texp
+ tmant += mant
+ # Round tmant * 2**texp to a float. The original recipe
+ # used float(str(tmant)) * 2.0**texp for this, but that's
+ # a little unsafe because str -> float conversion can't be
+ # relied upon to do correct rounding on all platforms.
+ tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
+ if tail > 0:
+ h = 1 << (tail-1)
+ tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
+ texp += tail
+ return math.ldexp(tmant, texp)
+
+ test_values = [
+ ([], 0.0),
+ ([0.0], 0.0),
+ ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),
+ ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),
+ ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),
+ ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),
+ ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),
+ ([1./n for n in range(1, 1001)],
+ float.fromhex('0x1.df11f45f4e61ap+2')),
+ ([(-1.)**n/n for n in range(1, 1001)],
+ float.fromhex('-0x1.62a2af1bd3624p-1')),
+ ([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0),
+ ([1e16, 1., 1e-16], 10000000000000002.0),
+ ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),
+ # exercise code for resizing partials array
+ ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +
+ [-2.**1022],
+ float.fromhex('0x1.5555555555555p+970')),
+ ]
+
+ for i, (vals, expected) in enumerate(test_values):
+ try:
+ actual = math.fsum(vals)
+ except OverflowError:
+ self.fail("test %d failed: got OverflowError, expected %r "
+ "for math.fsum(%.100r)" % (i, expected, vals))
+ except ValueError:
+ self.fail("test %d failed: got ValueError, expected %r "
+ "for math.fsum(%.100r)" % (i, expected, vals))
+ self.assertEqual(actual, expected)
+
+ from random import random, gauss, shuffle
+ for j in xrange(1000):
+ vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
+ s = 0
+ for i in xrange(200):
+ v = gauss(0, random()) ** 7 - s
+ s += v
+ vals.append(v)
+ shuffle(vals)
+
+ s = msum(vals)
+ self.assertEqual(msum(vals), math.fsum(vals))
+
+ 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.assert_(math.isnan(math.hypot(1.0, NAN)))
+ self.assert_(math.isnan(math.hypot(NAN, -2.0)))
+
+ 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.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)
+ 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)))
+
+ 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 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.assertEquals(math.log(INF), INF)
+ self.assertRaises(ValueError, math.log, NINF)
+ self.assert_(math.isnan(math.log(NAN)))
+
+ 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.assertEquals(math.log1p(INF), INF)
+ self.assertRaises(ValueError, math.log1p, NINF)
+ self.assert_(math.isnan(math.log1p(NAN)))
+ n= 2**90
+ self.assertAlmostEquals(math.log1p(n), 62.383246250395075)
+ self.assertAlmostEquals(math.log1p(n), math.log1p(float(n)))
+
+ 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.assertEquals(math.log(INF), INF)
+ self.assertRaises(ValueError, math.log10, NINF)
+ self.assert_(math.isnan(math.log10(NAN)))
+
+ def testModf(self):
+ self.assertRaises(TypeError, math.modf)
+
+ def testmodf(name, (v1, v2), (e1, e2)):
+ 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.assertEquals(math.modf(INF), (0.0, INF))
+ self.assertEquals(math.modf(NINF), (-0.0, NINF))
+
+ modf_nan = math.modf(NAN)
+ self.assert_(math.isnan(modf_nan[0]))
+ self.assert_(math.isnan(modf_nan[1]))
+
+ 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.assert_(math.isnan(math.pow(NAN, 1)))
+ self.assert_(math.isnan(math.pow(2, NAN)))
+ self.assert_(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.assert_(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.assert_(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.assert_(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.assert_(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.assert_(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)
+
+ # the following tests have been commented out since they don't
+ # really belong here: the implementation of ** for floats is
+ # independent of the implemention of math.pow
+ #self.assertEqual(1**NAN, 1)
+ #self.assertEqual(1**INF, 1)
+ #self.assertEqual(1**NINF, 1)
+ #self.assertEqual(1**0, 1)
+ #self.assertEqual(1.**NAN, 1)
+ #self.assertEqual(1.**INF, 1)
+ #self.assertEqual(1.**NINF, 1)
+ #self.assertEqual(1.**0, 1)
+
+ def testRadians(self):
+ self.assertRaises(TypeError, math.radians)
+ self.ftest('radians(180)', math.radians(180), math.pi)
+ self.ftest('radians(90)', math.radians(90), math.pi/2)
+ self.ftest('radians(-45)', math.radians(-45), -math.pi/4)
+
+ 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.assert_(math.isnan(math.sin(INF)))
+ self.assert_(math.isnan(math.sin(NINF)))
+ except ValueError:
+ self.assertRaises(ValueError, math.sin, INF)
+ self.assertRaises(ValueError, math.sin, NINF)
+ self.assert_(math.isnan(math.sin(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.assertEquals(math.sinh(INF), INF)
+ self.assertEquals(math.sinh(NINF), NINF)
+ self.assert_(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.assertEquals(math.sqrt(INF), INF)
+ self.assertRaises(ValueError, math.sqrt, NINF)
+ self.assert_(math.isnan(math.sqrt(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.assert_(math.isnan(math.tan(INF)))
+ self.assert_(math.isnan(math.tan(NINF)))
+ except:
+ self.assertRaises(ValueError, math.tan, INF)
+ self.assertRaises(ValueError, math.tan, NINF)
+ self.assert_(math.isnan(math.tan(NAN)))
+
+ 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.assert_(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 test_trunc(self):
+ self.assertEqual(math.trunc(1), 1)
+ self.assertEqual(math.trunc(-1), -1)
+ self.assertEqual(type(math.trunc(1)), int)
+ self.assertEqual(type(math.trunc(1.5)), int)
+ self.assertEqual(math.trunc(1.5), 1)
+ self.assertEqual(math.trunc(-1.5), -1)
+ self.assertEqual(math.trunc(1.999999), 1)
+ self.assertEqual(math.trunc(-1.999999), -1)
+ self.assertEqual(math.trunc(-0.999999), -0)
+ self.assertEqual(math.trunc(-100.999), -100)
+
+ class TestTrunc(object):
+ def __trunc__(self):
+ return 23
+
+ class TestNoTrunc(object):
+ pass
+
+ self.assertEqual(math.trunc(TestTrunc()), 23)
+
+ self.assertRaises(TypeError, math.trunc)
+ self.assertRaises(TypeError, math.trunc, 1, 2)
+ # XXX: This is not ideal, but see the comment in math_trunc().
+ self.assertRaises(AttributeError, math.trunc, TestNoTrunc())
+
+ t = TestNoTrunc()
+ t.__trunc__ = lambda *args: args
+ self.assertEquals((), math.trunc(t))
+ self.assertRaises(TypeError, math.trunc, t, 0)
+
+ 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)
+
+ def testIsnan(self):
+ self.assert_(math.isnan(float("nan")))
+ self.assert_(math.isnan(float("inf")* 0.))
+ self.failIf(math.isnan(float("inf")))
+ self.failIf(math.isnan(0.))
+ self.failIf(math.isnan(1.))
+
+ def testIsinf(self):
+ self.assert_(math.isinf(float("inf")))
+ self.assert_(math.isinf(float("-inf")))
+ self.assert_(math.isinf(1E400))
+ self.assert_(math.isinf(-1E400))
+ self.failIf(math.isinf(float("nan")))
+ self.failIf(math.isinf(0.))
+ self.failIf(math.isinf(1.))
+
+ # RED_FLAG 16-Oct-2000 Tim
+ # While 2.0 is more consistent about exceptions than previous releases, it
+ # still fails this part of the test on some platforms. For now, we only
+ # *run* test_exceptions() in verbose mode, so that this isn't normally
+ # tested.
+
+ if verbose:
+ def test_exceptions(self):
+ try:
+ x = math.exp(-1000000000)
+ except:
+ # mathmodule.c is failing to weed out underflows from libm, or
+ # we've got an fp format with huge dynamic range
+ self.fail("underflowing exp() should not have raised "
+ "an exception")
+ if x != 0:
+ self.fail("underflowing exp() should have returned 0")
+
+ # If this fails, probably using a strict IEEE-754 conforming libm, and x
+ # is +Inf afterwards. But Python wants overflows detected by default.
+ try:
+ x = math.exp(1000000000)
+ except OverflowError:
+ pass
+ else:
+ self.fail("overflowing exp() didn't trigger OverflowError")
+
+ # If this fails, it could be a puzzle. One odd possibility is that
+ # mathmodule.c's macros are getting confused while comparing
+ # Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE
+ # as a result (and so raising OverflowError instead).
+ try:
+ x = math.sqrt(-1.0)
+ except ValueError:
+ pass
+ else:
+ self.fail("sqrt(-1) didn't raise ValueError")
+
+ def test_testfile(self):
+ if not float.__getformat__("double").startswith("IEEE"):
+ return
+ for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):
+ # Skip if either the input or result is complex, or if
+ # flags is nonempty
+ if ai != 0. or ei != 0. or flags:
+ continue
+ if fn in ['rect', 'polar']:
+ # no real versions of rect, polar
+ continue
+ func = getattr(math, fn)
+ try:
+ result = func(ar)
+ except ValueError:
+ message = ("Unexpected ValueError in " +
+ "test %s:%s(%r)\n" % (id, fn, ar))
+ self.fail(message)
+ except OverflowError:
+ message = ("Unexpected OverflowError in " +
+ "test %s:%s(%r)\n" % (id, fn, ar))
+ self.fail(message)
+ self.ftest("%s:%s(%r)" % (id, fn, ar), result, er)
+
+def test_main():
+ from doctest import DocFileSuite
+ suite = unittest.TestSuite()
+ suite.addTest(unittest.makeSuite(MathTests))
+ suite.addTest(DocFileSuite("ieee754.txt"))
+ run_unittest(suite)
+
+if __name__ == '__main__':
+ test_main()