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-# 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
-import struct
-
-eps = 1E-05
-NAN = float('nan')
-INF = float('inf')
-NINF = float('-inf')
-
-# decorator for skipping tests on non-IEEE 754 platforms
-requires_IEEE_754 = unittest.skipUnless(
- float.__getformat__("double").startswith("IEEE"),
- "test requires IEEE 754 doubles")
-
-# detect evidence of double-rounding: fsum is not always correctly
-# rounded on machines that suffer from double rounding.
-x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer
-HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4)
-
-# locate file with test values
-if __name__ == '__main__':
- file = sys.argv[0]
-else:
- file = __file__
-test_dir = os.path.dirname(file) or os.curdir
-math_testcases = os.path.join(test_dir, 'math_testcases.txt')
-test_file = os.path.join(test_dir, 'cmath_testcases.txt')
-
-def to_ulps(x):
- """Convert a non-NaN float x to an integer, in such a way that
- adjacent floats are converted to adjacent integers. Then
- abs(ulps(x) - ulps(y)) gives the difference in ulps between two
- floats.
-
- The results from this function will only make sense on platforms
- where C doubles are represented in IEEE 754 binary64 format.
-
- """
- n = struct.unpack('<q', struct.pack('<d', x))[0]
- if n < 0:
- n = ~(n+2**63)
- return n
-
-def ulps_check(expected, got, ulps=20):
- """Given non-NaN floats `expected` and `got`,
- check that they're equal to within the given number of ulps.
-
- Returns None on success and an error message on failure."""
-
- ulps_error = to_ulps(got) - to_ulps(expected)
- if abs(ulps_error) <= ulps:
- return None
- return "error = {} ulps; permitted error = {} ulps".format(ulps_error,
- ulps)
-
-def acc_check(expected, got, rel_err=2e-15, abs_err = 5e-323):
- """Determine whether non-NaN floats 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."""
-
- # need to special case infinities, since inf - inf gives nan
- if math.isinf(expected) and got == expected:
- return None
-
- error = got - expected
-
- permitted_error = max(abs_err, rel_err * abs(expected))
- if abs(error) < permitted_error:
- return None
- return "error = {}; permitted error = {}".format(error,
- permitted_error)
-
-def parse_mtestfile(fname):
- """Parse a file with test values
-
- -- starts a comment
- blank lines, or lines containing only a comment, are ignored
- other lines are expected to have the form
- id fn arg -> expected [flag]*
-
- """
- with open(fname) as fp:
- for line in fp:
- # strip comments, and skip blank lines
- if '--' in line:
- line = line[:line.index('--')]
- if not line.strip():
- continue
-
- lhs, rhs = line.split('->')
- id, fn, arg = lhs.split()
- rhs_pieces = rhs.split()
- exp = rhs_pieces[0]
- flags = rhs_pieces[1:]
-
- yield (id, fn, float(arg), float(exp), flags)
-
-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.assertTrue(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.assertEqual(math.acosh(INF), INF)
- self.assertRaises(ValueError, math.acosh, NINF)
- self.assertTrue(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.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 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 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 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 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)
-
- @requires_IEEE_754
- 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 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 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 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.assertEqual(math.exp(INF), INF)
- self.assertEqual(math.exp(NINF), 0.)
- self.assertTrue(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 values:
- 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.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 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 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]))
-
- @requires_IEEE_754
- @unittest.skipIf(HAVE_DOUBLE_ROUNDING,
- "fsum is not exact on machines with double rounding")
- 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.
-
- # 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.assertTrue(math.isnan(math.hypot(1.0, NAN)))
- self.assertTrue(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.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 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 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 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 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 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)
-
- # the following tests have been commented out since they don't
- # really belong here: the implementation of ** for floats is
- # independent of the implementation 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.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 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 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 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 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)
- self.assertRaises((AttributeError, TypeError), math.trunc,
- TestNoTrunc())
-
- 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 testIsinf(self):
- self.assertTrue(math.isinf(float("inf")))
- self.assertTrue(math.isinf(float("-inf")))
- self.assertTrue(math.isinf(1E400))
- self.assertTrue(math.isinf(-1E400))
- self.assertFalse(math.isinf(float("nan")))
- self.assertFalse(math.isinf(0.))
- self.assertFalse(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")
-
- @requires_IEEE_754
- def test_testfile(self):
- 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)
-
- @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
- "test requires IEEE 754 doubles")
- 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 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()
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-07 02:50:44 +0000