+++ /dev/null
-# Python test set -- math module\r
-# XXXX Should not do tests around zero only\r
-\r
-from test.test_support import run_unittest, verbose\r
-import unittest\r
-import math\r
-import os\r
-import sys\r
-import random\r
-import struct\r
-\r
-eps = 1E-05\r
-NAN = float('nan')\r
-INF = float('inf')\r
-NINF = float('-inf')\r
-\r
-# decorator for skipping tests on non-IEEE 754 platforms\r
-requires_IEEE_754 = unittest.skipUnless(\r
- float.__getformat__("double").startswith("IEEE"),\r
- "test requires IEEE 754 doubles")\r
-\r
-# detect evidence of double-rounding: fsum is not always correctly\r
-# rounded on machines that suffer from double rounding.\r
-x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer\r
-HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4)\r
-\r
-# locate file with test values\r
-if __name__ == '__main__':\r
- file = sys.argv[0]\r
-else:\r
- file = __file__\r
-test_dir = os.path.dirname(file) or os.curdir\r
-math_testcases = os.path.join(test_dir, 'math_testcases.txt')\r
-test_file = os.path.join(test_dir, 'cmath_testcases.txt')\r
-\r
-def to_ulps(x):\r
- """Convert a non-NaN float x to an integer, in such a way that\r
- adjacent floats are converted to adjacent integers. Then\r
- abs(ulps(x) - ulps(y)) gives the difference in ulps between two\r
- floats.\r
-\r
- The results from this function will only make sense on platforms\r
- where C doubles are represented in IEEE 754 binary64 format.\r
-\r
- """\r
- n = struct.unpack('<q', struct.pack('<d', x))[0]\r
- if n < 0:\r
- n = ~(n+2**63)\r
- return n\r
-\r
-def ulps_check(expected, got, ulps=20):\r
- """Given non-NaN floats `expected` and `got`,\r
- check that they're equal to within the given number of ulps.\r
-\r
- Returns None on success and an error message on failure."""\r
-\r
- ulps_error = to_ulps(got) - to_ulps(expected)\r
- if abs(ulps_error) <= ulps:\r
- return None\r
- return "error = {} ulps; permitted error = {} ulps".format(ulps_error,\r
- ulps)\r
-\r
-def acc_check(expected, got, rel_err=2e-15, abs_err = 5e-323):\r
- """Determine whether non-NaN floats a and b are equal to within a\r
- (small) rounding error. The default values for rel_err and\r
- abs_err are chosen to be suitable for platforms where a float is\r
- represented by an IEEE 754 double. They allow an error of between\r
- 9 and 19 ulps."""\r
-\r
- # need to special case infinities, since inf - inf gives nan\r
- if math.isinf(expected) and got == expected:\r
- return None\r
-\r
- error = got - expected\r
-\r
- permitted_error = max(abs_err, rel_err * abs(expected))\r
- if abs(error) < permitted_error:\r
- return None\r
- return "error = {}; permitted error = {}".format(error,\r
- permitted_error)\r
-\r
-def parse_mtestfile(fname):\r
- """Parse a file with test values\r
-\r
- -- starts a comment\r
- blank lines, or lines containing only a comment, are ignored\r
- other lines are expected to have the form\r
- id fn arg -> expected [flag]*\r
-\r
- """\r
- with open(fname) as fp:\r
- for line in fp:\r
- # strip comments, and skip blank lines\r
- if '--' in line:\r
- line = line[:line.index('--')]\r
- if not line.strip():\r
- continue\r
-\r
- lhs, rhs = line.split('->')\r
- id, fn, arg = lhs.split()\r
- rhs_pieces = rhs.split()\r
- exp = rhs_pieces[0]\r
- flags = rhs_pieces[1:]\r
-\r
- yield (id, fn, float(arg), float(exp), flags)\r
-\r
-def parse_testfile(fname):\r
- """Parse a file with test values\r
-\r
- Empty lines or lines starting with -- are ignored\r
- yields id, fn, arg_real, arg_imag, exp_real, exp_imag\r
- """\r
- with open(fname) as fp:\r
- for line in fp:\r
- # skip comment lines and blank lines\r
- if line.startswith('--') or not line.strip():\r
- continue\r
-\r
- lhs, rhs = line.split('->')\r
- id, fn, arg_real, arg_imag = lhs.split()\r
- rhs_pieces = rhs.split()\r
- exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1]\r
- flags = rhs_pieces[2:]\r
-\r
- yield (id, fn,\r
- float(arg_real), float(arg_imag),\r
- float(exp_real), float(exp_imag),\r
- flags\r
- )\r
-\r
-class MathTests(unittest.TestCase):\r
-\r
- def ftest(self, name, value, expected):\r
- if abs(value-expected) > eps:\r
- # Use %r instead of %f so the error message\r
- # displays full precision. Otherwise discrepancies\r
- # in the last few bits will lead to very confusing\r
- # error messages\r
- self.fail('%s returned %r, expected %r' %\r
- (name, value, expected))\r
-\r
- def testConstants(self):\r
- self.ftest('pi', math.pi, 3.1415926)\r
- self.ftest('e', math.e, 2.7182818)\r
-\r
- def testAcos(self):\r
- self.assertRaises(TypeError, math.acos)\r
- self.ftest('acos(-1)', math.acos(-1), math.pi)\r
- self.ftest('acos(0)', math.acos(0), math.pi/2)\r
- self.ftest('acos(1)', math.acos(1), 0)\r
- self.assertRaises(ValueError, math.acos, INF)\r
- self.assertRaises(ValueError, math.acos, NINF)\r
- self.assertTrue(math.isnan(math.acos(NAN)))\r
-\r
- def testAcosh(self):\r
- self.assertRaises(TypeError, math.acosh)\r
- self.ftest('acosh(1)', math.acosh(1), 0)\r
- self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168)\r
- self.assertRaises(ValueError, math.acosh, 0)\r
- self.assertRaises(ValueError, math.acosh, -1)\r
- self.assertEqual(math.acosh(INF), INF)\r
- self.assertRaises(ValueError, math.acosh, NINF)\r
- self.assertTrue(math.isnan(math.acosh(NAN)))\r
-\r
- def testAsin(self):\r
- self.assertRaises(TypeError, math.asin)\r
- self.ftest('asin(-1)', math.asin(-1), -math.pi/2)\r
- self.ftest('asin(0)', math.asin(0), 0)\r
- self.ftest('asin(1)', math.asin(1), math.pi/2)\r
- self.assertRaises(ValueError, math.asin, INF)\r
- self.assertRaises(ValueError, math.asin, NINF)\r
- self.assertTrue(math.isnan(math.asin(NAN)))\r
-\r
- def testAsinh(self):\r
- self.assertRaises(TypeError, math.asinh)\r
- self.ftest('asinh(0)', math.asinh(0), 0)\r
- self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305)\r
- self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305)\r
- self.assertEqual(math.asinh(INF), INF)\r
- self.assertEqual(math.asinh(NINF), NINF)\r
- self.assertTrue(math.isnan(math.asinh(NAN)))\r
-\r
- def testAtan(self):\r
- self.assertRaises(TypeError, math.atan)\r
- self.ftest('atan(-1)', math.atan(-1), -math.pi/4)\r
- self.ftest('atan(0)', math.atan(0), 0)\r
- self.ftest('atan(1)', math.atan(1), math.pi/4)\r
- self.ftest('atan(inf)', math.atan(INF), math.pi/2)\r
- self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2)\r
- self.assertTrue(math.isnan(math.atan(NAN)))\r
-\r
- def testAtanh(self):\r
- self.assertRaises(TypeError, math.atan)\r
- self.ftest('atanh(0)', math.atanh(0), 0)\r
- self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489)\r
- self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489)\r
- self.assertRaises(ValueError, math.atanh, 1)\r
- self.assertRaises(ValueError, math.atanh, -1)\r
- self.assertRaises(ValueError, math.atanh, INF)\r
- self.assertRaises(ValueError, math.atanh, NINF)\r
- self.assertTrue(math.isnan(math.atanh(NAN)))\r
-\r
- def testAtan2(self):\r
- self.assertRaises(TypeError, math.atan2)\r
- self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2)\r
- self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4)\r
- self.ftest('atan2(0, 1)', math.atan2(0, 1), 0)\r
- self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4)\r
- self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2)\r
-\r
- # math.atan2(0, x)\r
- self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi)\r
- self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi)\r
- self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi)\r
- self.assertEqual(math.atan2(0., 0.), 0.)\r
- self.assertEqual(math.atan2(0., 2.3), 0.)\r
- self.assertEqual(math.atan2(0., INF), 0.)\r
- self.assertTrue(math.isnan(math.atan2(0., NAN)))\r
- # math.atan2(-0, x)\r
- self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi)\r
- self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi)\r
- self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi)\r
- self.assertEqual(math.atan2(-0., 0.), -0.)\r
- self.assertEqual(math.atan2(-0., 2.3), -0.)\r
- self.assertEqual(math.atan2(-0., INF), -0.)\r
- self.assertTrue(math.isnan(math.atan2(-0., NAN)))\r
- # math.atan2(INF, x)\r
- self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4)\r
- self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2)\r
- self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2)\r
- self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2)\r
- self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2)\r
- self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4)\r
- self.assertTrue(math.isnan(math.atan2(INF, NAN)))\r
- # math.atan2(NINF, x)\r
- self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4)\r
- self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2)\r
- self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2)\r
- self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2)\r
- self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2)\r
- self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4)\r
- self.assertTrue(math.isnan(math.atan2(NINF, NAN)))\r
- # math.atan2(+finite, x)\r
- self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi)\r
- self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2)\r
- self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2)\r
- self.assertEqual(math.atan2(2.3, INF), 0.)\r
- self.assertTrue(math.isnan(math.atan2(2.3, NAN)))\r
- # math.atan2(-finite, x)\r
- self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi)\r
- self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2)\r
- self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2)\r
- self.assertEqual(math.atan2(-2.3, INF), -0.)\r
- self.assertTrue(math.isnan(math.atan2(-2.3, NAN)))\r
- # math.atan2(NAN, x)\r
- self.assertTrue(math.isnan(math.atan2(NAN, NINF)))\r
- self.assertTrue(math.isnan(math.atan2(NAN, -2.3)))\r
- self.assertTrue(math.isnan(math.atan2(NAN, -0.)))\r
- self.assertTrue(math.isnan(math.atan2(NAN, 0.)))\r
- self.assertTrue(math.isnan(math.atan2(NAN, 2.3)))\r
- self.assertTrue(math.isnan(math.atan2(NAN, INF)))\r
- self.assertTrue(math.isnan(math.atan2(NAN, NAN)))\r
-\r
- def testCeil(self):\r
- self.assertRaises(TypeError, math.ceil)\r
- # These types will be int in py3k.\r
- self.assertEqual(float, type(math.ceil(1)))\r
- self.assertEqual(float, type(math.ceil(1L)))\r
- self.assertEqual(float, type(math.ceil(1.0)))\r
- self.ftest('ceil(0.5)', math.ceil(0.5), 1)\r
- self.ftest('ceil(1.0)', math.ceil(1.0), 1)\r
- self.ftest('ceil(1.5)', math.ceil(1.5), 2)\r
- self.ftest('ceil(-0.5)', math.ceil(-0.5), 0)\r
- self.ftest('ceil(-1.0)', math.ceil(-1.0), -1)\r
- self.ftest('ceil(-1.5)', math.ceil(-1.5), -1)\r
- self.assertEqual(math.ceil(INF), INF)\r
- self.assertEqual(math.ceil(NINF), NINF)\r
- self.assertTrue(math.isnan(math.ceil(NAN)))\r
-\r
- class TestCeil(object):\r
- def __float__(self):\r
- return 41.3\r
- class TestNoCeil(object):\r
- pass\r
- self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42)\r
- self.assertRaises(TypeError, math.ceil, TestNoCeil())\r
-\r
- t = TestNoCeil()\r
- t.__ceil__ = lambda *args: args\r
- self.assertRaises(TypeError, math.ceil, t)\r
- self.assertRaises(TypeError, math.ceil, t, 0)\r
-\r
- @requires_IEEE_754\r
- def testCopysign(self):\r
- self.assertEqual(math.copysign(1, 42), 1.0)\r
- self.assertEqual(math.copysign(0., 42), 0.0)\r
- self.assertEqual(math.copysign(1., -42), -1.0)\r
- self.assertEqual(math.copysign(3, 0.), 3.0)\r
- self.assertEqual(math.copysign(4., -0.), -4.0)\r
-\r
- self.assertRaises(TypeError, math.copysign)\r
- # copysign should let us distinguish signs of zeros\r
- self.assertEqual(math.copysign(1., 0.), 1.)\r
- self.assertEqual(math.copysign(1., -0.), -1.)\r
- self.assertEqual(math.copysign(INF, 0.), INF)\r
- self.assertEqual(math.copysign(INF, -0.), NINF)\r
- self.assertEqual(math.copysign(NINF, 0.), INF)\r
- self.assertEqual(math.copysign(NINF, -0.), NINF)\r
- # and of infinities\r
- self.assertEqual(math.copysign(1., INF), 1.)\r
- self.assertEqual(math.copysign(1., NINF), -1.)\r
- self.assertEqual(math.copysign(INF, INF), INF)\r
- self.assertEqual(math.copysign(INF, NINF), NINF)\r
- self.assertEqual(math.copysign(NINF, INF), INF)\r
- self.assertEqual(math.copysign(NINF, NINF), NINF)\r
- self.assertTrue(math.isnan(math.copysign(NAN, 1.)))\r
- self.assertTrue(math.isnan(math.copysign(NAN, INF)))\r
- self.assertTrue(math.isnan(math.copysign(NAN, NINF)))\r
- self.assertTrue(math.isnan(math.copysign(NAN, NAN)))\r
- # copysign(INF, NAN) may be INF or it may be NINF, since\r
- # we don't know whether the sign bit of NAN is set on any\r
- # given platform.\r
- self.assertTrue(math.isinf(math.copysign(INF, NAN)))\r
- # similarly, copysign(2., NAN) could be 2. or -2.\r
- self.assertEqual(abs(math.copysign(2., NAN)), 2.)\r
-\r
- def testCos(self):\r
- self.assertRaises(TypeError, math.cos)\r
- self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0)\r
- self.ftest('cos(0)', math.cos(0), 1)\r
- self.ftest('cos(pi/2)', math.cos(math.pi/2), 0)\r
- self.ftest('cos(pi)', math.cos(math.pi), -1)\r
- try:\r
- self.assertTrue(math.isnan(math.cos(INF)))\r
- self.assertTrue(math.isnan(math.cos(NINF)))\r
- except ValueError:\r
- self.assertRaises(ValueError, math.cos, INF)\r
- self.assertRaises(ValueError, math.cos, NINF)\r
- self.assertTrue(math.isnan(math.cos(NAN)))\r
-\r
- def testCosh(self):\r
- self.assertRaises(TypeError, math.cosh)\r
- self.ftest('cosh(0)', math.cosh(0), 1)\r
- self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert\r
- self.assertEqual(math.cosh(INF), INF)\r
- self.assertEqual(math.cosh(NINF), INF)\r
- self.assertTrue(math.isnan(math.cosh(NAN)))\r
-\r
- def testDegrees(self):\r
- self.assertRaises(TypeError, math.degrees)\r
- self.ftest('degrees(pi)', math.degrees(math.pi), 180.0)\r
- self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0)\r
- self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0)\r
-\r
- def testExp(self):\r
- self.assertRaises(TypeError, math.exp)\r
- self.ftest('exp(-1)', math.exp(-1), 1/math.e)\r
- self.ftest('exp(0)', math.exp(0), 1)\r
- self.ftest('exp(1)', math.exp(1), math.e)\r
- self.assertEqual(math.exp(INF), INF)\r
- self.assertEqual(math.exp(NINF), 0.)\r
- self.assertTrue(math.isnan(math.exp(NAN)))\r
-\r
- def testFabs(self):\r
- self.assertRaises(TypeError, math.fabs)\r
- self.ftest('fabs(-1)', math.fabs(-1), 1)\r
- self.ftest('fabs(0)', math.fabs(0), 0)\r
- self.ftest('fabs(1)', math.fabs(1), 1)\r
-\r
- def testFactorial(self):\r
- def fact(n):\r
- result = 1\r
- for i in range(1, int(n)+1):\r
- result *= i\r
- return result\r
- values = range(10) + [50, 100, 500]\r
- random.shuffle(values)\r
- for x in values:\r
- for cast in (int, long, float):\r
- self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x)))\r
- self.assertRaises(ValueError, math.factorial, -1)\r
- self.assertRaises(ValueError, math.factorial, math.pi)\r
-\r
- def testFloor(self):\r
- self.assertRaises(TypeError, math.floor)\r
- # These types will be int in py3k.\r
- self.assertEqual(float, type(math.floor(1)))\r
- self.assertEqual(float, type(math.floor(1L)))\r
- self.assertEqual(float, type(math.floor(1.0)))\r
- self.ftest('floor(0.5)', math.floor(0.5), 0)\r
- self.ftest('floor(1.0)', math.floor(1.0), 1)\r
- self.ftest('floor(1.5)', math.floor(1.5), 1)\r
- self.ftest('floor(-0.5)', math.floor(-0.5), -1)\r
- self.ftest('floor(-1.0)', math.floor(-1.0), -1)\r
- self.ftest('floor(-1.5)', math.floor(-1.5), -2)\r
- # pow() relies on floor() to check for integers\r
- # This fails on some platforms - so check it here\r
- self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167)\r
- self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167)\r
- self.assertEqual(math.ceil(INF), INF)\r
- self.assertEqual(math.ceil(NINF), NINF)\r
- self.assertTrue(math.isnan(math.floor(NAN)))\r
-\r
- class TestFloor(object):\r
- def __float__(self):\r
- return 42.3\r
- class TestNoFloor(object):\r
- pass\r
- self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42)\r
- self.assertRaises(TypeError, math.floor, TestNoFloor())\r
-\r
- t = TestNoFloor()\r
- t.__floor__ = lambda *args: args\r
- self.assertRaises(TypeError, math.floor, t)\r
- self.assertRaises(TypeError, math.floor, t, 0)\r
-\r
- def testFmod(self):\r
- self.assertRaises(TypeError, math.fmod)\r
- self.ftest('fmod(10,1)', math.fmod(10,1), 0)\r
- self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0)\r
- self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1)\r
- self.ftest('fmod(-10,1)', math.fmod(-10,1), 0)\r
- self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0)\r
- self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1)\r
- self.assertTrue(math.isnan(math.fmod(NAN, 1.)))\r
- self.assertTrue(math.isnan(math.fmod(1., NAN)))\r
- self.assertTrue(math.isnan(math.fmod(NAN, NAN)))\r
- self.assertRaises(ValueError, math.fmod, 1., 0.)\r
- self.assertRaises(ValueError, math.fmod, INF, 1.)\r
- self.assertRaises(ValueError, math.fmod, NINF, 1.)\r
- self.assertRaises(ValueError, math.fmod, INF, 0.)\r
- self.assertEqual(math.fmod(3.0, INF), 3.0)\r
- self.assertEqual(math.fmod(-3.0, INF), -3.0)\r
- self.assertEqual(math.fmod(3.0, NINF), 3.0)\r
- self.assertEqual(math.fmod(-3.0, NINF), -3.0)\r
- self.assertEqual(math.fmod(0.0, 3.0), 0.0)\r
- self.assertEqual(math.fmod(0.0, NINF), 0.0)\r
-\r
- def testFrexp(self):\r
- self.assertRaises(TypeError, math.frexp)\r
-\r
- def testfrexp(name, result, expected):\r
- (mant, exp), (emant, eexp) = result, expected\r
- if abs(mant-emant) > eps or exp != eexp:\r
- self.fail('%s returned %r, expected %r'%\\r
- (name, (mant, exp), (emant,eexp)))\r
-\r
- testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1))\r
- testfrexp('frexp(0)', math.frexp(0), (0, 0))\r
- testfrexp('frexp(1)', math.frexp(1), (0.5, 1))\r
- testfrexp('frexp(2)', math.frexp(2), (0.5, 2))\r
-\r
- self.assertEqual(math.frexp(INF)[0], INF)\r
- self.assertEqual(math.frexp(NINF)[0], NINF)\r
- self.assertTrue(math.isnan(math.frexp(NAN)[0]))\r
-\r
- @requires_IEEE_754\r
- @unittest.skipIf(HAVE_DOUBLE_ROUNDING,\r
- "fsum is not exact on machines with double rounding")\r
- def testFsum(self):\r
- # math.fsum relies on exact rounding for correct operation.\r
- # There's a known problem with IA32 floating-point that causes\r
- # inexact rounding in some situations, and will cause the\r
- # math.fsum tests below to fail; see issue #2937. On non IEEE\r
- # 754 platforms, and on IEEE 754 platforms that exhibit the\r
- # problem described in issue #2937, we simply skip the whole\r
- # test.\r
-\r
- # Python version of math.fsum, for comparison. Uses a\r
- # different algorithm based on frexp, ldexp and integer\r
- # arithmetic.\r
- from sys import float_info\r
- mant_dig = float_info.mant_dig\r
- etiny = float_info.min_exp - mant_dig\r
-\r
- def msum(iterable):\r
- """Full precision summation. Compute sum(iterable) without any\r
- intermediate accumulation of error. Based on the 'lsum' function\r
- at http://code.activestate.com/recipes/393090/\r
-\r
- """\r
- tmant, texp = 0, 0\r
- for x in iterable:\r
- mant, exp = math.frexp(x)\r
- mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig\r
- if texp > exp:\r
- tmant <<= texp-exp\r
- texp = exp\r
- else:\r
- mant <<= exp-texp\r
- tmant += mant\r
- # Round tmant * 2**texp to a float. The original recipe\r
- # used float(str(tmant)) * 2.0**texp for this, but that's\r
- # a little unsafe because str -> float conversion can't be\r
- # relied upon to do correct rounding on all platforms.\r
- tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)\r
- if tail > 0:\r
- h = 1 << (tail-1)\r
- tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)\r
- texp += tail\r
- return math.ldexp(tmant, texp)\r
-\r
- test_values = [\r
- ([], 0.0),\r
- ([0.0], 0.0),\r
- ([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100),\r
- ([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0),\r
- ([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0),\r
- ([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0),\r
- ([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0),\r
- ([1./n for n in range(1, 1001)],\r
- float.fromhex('0x1.df11f45f4e61ap+2')),\r
- ([(-1.)**n/n for n in range(1, 1001)],\r
- float.fromhex('-0x1.62a2af1bd3624p-1')),\r
- ([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0),\r
- ([1e16, 1., 1e-16], 10000000000000002.0),\r
- ([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0),\r
- # exercise code for resizing partials array\r
- ([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] +\r
- [-2.**1022],\r
- float.fromhex('0x1.5555555555555p+970')),\r
- ]\r
-\r
- for i, (vals, expected) in enumerate(test_values):\r
- try:\r
- actual = math.fsum(vals)\r
- except OverflowError:\r
- self.fail("test %d failed: got OverflowError, expected %r "\r
- "for math.fsum(%.100r)" % (i, expected, vals))\r
- except ValueError:\r
- self.fail("test %d failed: got ValueError, expected %r "\r
- "for math.fsum(%.100r)" % (i, expected, vals))\r
- self.assertEqual(actual, expected)\r
-\r
- from random import random, gauss, shuffle\r
- for j in xrange(1000):\r
- vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10\r
- s = 0\r
- for i in xrange(200):\r
- v = gauss(0, random()) ** 7 - s\r
- s += v\r
- vals.append(v)\r
- shuffle(vals)\r
-\r
- s = msum(vals)\r
- self.assertEqual(msum(vals), math.fsum(vals))\r
-\r
- def testHypot(self):\r
- self.assertRaises(TypeError, math.hypot)\r
- self.ftest('hypot(0,0)', math.hypot(0,0), 0)\r
- self.ftest('hypot(3,4)', math.hypot(3,4), 5)\r
- self.assertEqual(math.hypot(NAN, INF), INF)\r
- self.assertEqual(math.hypot(INF, NAN), INF)\r
- self.assertEqual(math.hypot(NAN, NINF), INF)\r
- self.assertEqual(math.hypot(NINF, NAN), INF)\r
- self.assertTrue(math.isnan(math.hypot(1.0, NAN)))\r
- self.assertTrue(math.isnan(math.hypot(NAN, -2.0)))\r
-\r
- def testLdexp(self):\r
- self.assertRaises(TypeError, math.ldexp)\r
- self.ftest('ldexp(0,1)', math.ldexp(0,1), 0)\r
- self.ftest('ldexp(1,1)', math.ldexp(1,1), 2)\r
- self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5)\r
- self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2)\r
- self.assertRaises(OverflowError, math.ldexp, 1., 1000000)\r
- self.assertRaises(OverflowError, math.ldexp, -1., 1000000)\r
- self.assertEqual(math.ldexp(1., -1000000), 0.)\r
- self.assertEqual(math.ldexp(-1., -1000000), -0.)\r
- self.assertEqual(math.ldexp(INF, 30), INF)\r
- self.assertEqual(math.ldexp(NINF, -213), NINF)\r
- self.assertTrue(math.isnan(math.ldexp(NAN, 0)))\r
-\r
- # large second argument\r
- for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]:\r
- self.assertEqual(math.ldexp(INF, -n), INF)\r
- self.assertEqual(math.ldexp(NINF, -n), NINF)\r
- self.assertEqual(math.ldexp(1., -n), 0.)\r
- self.assertEqual(math.ldexp(-1., -n), -0.)\r
- self.assertEqual(math.ldexp(0., -n), 0.)\r
- self.assertEqual(math.ldexp(-0., -n), -0.)\r
- self.assertTrue(math.isnan(math.ldexp(NAN, -n)))\r
-\r
- self.assertRaises(OverflowError, math.ldexp, 1., n)\r
- self.assertRaises(OverflowError, math.ldexp, -1., n)\r
- self.assertEqual(math.ldexp(0., n), 0.)\r
- self.assertEqual(math.ldexp(-0., n), -0.)\r
- self.assertEqual(math.ldexp(INF, n), INF)\r
- self.assertEqual(math.ldexp(NINF, n), NINF)\r
- self.assertTrue(math.isnan(math.ldexp(NAN, n)))\r
-\r
- def testLog(self):\r
- self.assertRaises(TypeError, math.log)\r
- self.ftest('log(1/e)', math.log(1/math.e), -1)\r
- self.ftest('log(1)', math.log(1), 0)\r
- self.ftest('log(e)', math.log(math.e), 1)\r
- self.ftest('log(32,2)', math.log(32,2), 5)\r
- self.ftest('log(10**40, 10)', math.log(10**40, 10), 40)\r
- self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2)\r
- self.assertEqual(math.log(INF), INF)\r
- self.assertRaises(ValueError, math.log, NINF)\r
- self.assertTrue(math.isnan(math.log(NAN)))\r
-\r
- def testLog1p(self):\r
- self.assertRaises(TypeError, math.log1p)\r
- self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1)\r
- self.ftest('log1p(0)', math.log1p(0), 0)\r
- self.ftest('log1p(e-1)', math.log1p(math.e-1), 1)\r
- self.ftest('log1p(1)', math.log1p(1), math.log(2))\r
- self.assertEqual(math.log1p(INF), INF)\r
- self.assertRaises(ValueError, math.log1p, NINF)\r
- self.assertTrue(math.isnan(math.log1p(NAN)))\r
- n= 2**90\r
- self.assertAlmostEqual(math.log1p(n), 62.383246250395075)\r
- self.assertAlmostEqual(math.log1p(n), math.log1p(float(n)))\r
-\r
- def testLog10(self):\r
- self.assertRaises(TypeError, math.log10)\r
- self.ftest('log10(0.1)', math.log10(0.1), -1)\r
- self.ftest('log10(1)', math.log10(1), 0)\r
- self.ftest('log10(10)', math.log10(10), 1)\r
- self.assertEqual(math.log(INF), INF)\r
- self.assertRaises(ValueError, math.log10, NINF)\r
- self.assertTrue(math.isnan(math.log10(NAN)))\r
-\r
- def testModf(self):\r
- self.assertRaises(TypeError, math.modf)\r
-\r
- def testmodf(name, result, expected):\r
- (v1, v2), (e1, e2) = result, expected\r
- if abs(v1-e1) > eps or abs(v2-e2):\r
- self.fail('%s returned %r, expected %r'%\\r
- (name, (v1,v2), (e1,e2)))\r
-\r
- testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0))\r
- testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0))\r
-\r
- self.assertEqual(math.modf(INF), (0.0, INF))\r
- self.assertEqual(math.modf(NINF), (-0.0, NINF))\r
-\r
- modf_nan = math.modf(NAN)\r
- self.assertTrue(math.isnan(modf_nan[0]))\r
- self.assertTrue(math.isnan(modf_nan[1]))\r
-\r
- def testPow(self):\r
- self.assertRaises(TypeError, math.pow)\r
- self.ftest('pow(0,1)', math.pow(0,1), 0)\r
- self.ftest('pow(1,0)', math.pow(1,0), 1)\r
- self.ftest('pow(2,1)', math.pow(2,1), 2)\r
- self.ftest('pow(2,-1)', math.pow(2,-1), 0.5)\r
- self.assertEqual(math.pow(INF, 1), INF)\r
- self.assertEqual(math.pow(NINF, 1), NINF)\r
- self.assertEqual((math.pow(1, INF)), 1.)\r
- self.assertEqual((math.pow(1, NINF)), 1.)\r
- self.assertTrue(math.isnan(math.pow(NAN, 1)))\r
- self.assertTrue(math.isnan(math.pow(2, NAN)))\r
- self.assertTrue(math.isnan(math.pow(0, NAN)))\r
- self.assertEqual(math.pow(1, NAN), 1)\r
-\r
- # pow(0., x)\r
- self.assertEqual(math.pow(0., INF), 0.)\r
- self.assertEqual(math.pow(0., 3.), 0.)\r
- self.assertEqual(math.pow(0., 2.3), 0.)\r
- self.assertEqual(math.pow(0., 2.), 0.)\r
- self.assertEqual(math.pow(0., 0.), 1.)\r
- self.assertEqual(math.pow(0., -0.), 1.)\r
- self.assertRaises(ValueError, math.pow, 0., -2.)\r
- self.assertRaises(ValueError, math.pow, 0., -2.3)\r
- self.assertRaises(ValueError, math.pow, 0., -3.)\r
- self.assertRaises(ValueError, math.pow, 0., NINF)\r
- self.assertTrue(math.isnan(math.pow(0., NAN)))\r
-\r
- # pow(INF, x)\r
- self.assertEqual(math.pow(INF, INF), INF)\r
- self.assertEqual(math.pow(INF, 3.), INF)\r
- self.assertEqual(math.pow(INF, 2.3), INF)\r
- self.assertEqual(math.pow(INF, 2.), INF)\r
- self.assertEqual(math.pow(INF, 0.), 1.)\r
- self.assertEqual(math.pow(INF, -0.), 1.)\r
- self.assertEqual(math.pow(INF, -2.), 0.)\r
- self.assertEqual(math.pow(INF, -2.3), 0.)\r
- self.assertEqual(math.pow(INF, -3.), 0.)\r
- self.assertEqual(math.pow(INF, NINF), 0.)\r
- self.assertTrue(math.isnan(math.pow(INF, NAN)))\r
-\r
- # pow(-0., x)\r
- self.assertEqual(math.pow(-0., INF), 0.)\r
- self.assertEqual(math.pow(-0., 3.), -0.)\r
- self.assertEqual(math.pow(-0., 2.3), 0.)\r
- self.assertEqual(math.pow(-0., 2.), 0.)\r
- self.assertEqual(math.pow(-0., 0.), 1.)\r
- self.assertEqual(math.pow(-0., -0.), 1.)\r
- self.assertRaises(ValueError, math.pow, -0., -2.)\r
- self.assertRaises(ValueError, math.pow, -0., -2.3)\r
- self.assertRaises(ValueError, math.pow, -0., -3.)\r
- self.assertRaises(ValueError, math.pow, -0., NINF)\r
- self.assertTrue(math.isnan(math.pow(-0., NAN)))\r
-\r
- # pow(NINF, x)\r
- self.assertEqual(math.pow(NINF, INF), INF)\r
- self.assertEqual(math.pow(NINF, 3.), NINF)\r
- self.assertEqual(math.pow(NINF, 2.3), INF)\r
- self.assertEqual(math.pow(NINF, 2.), INF)\r
- self.assertEqual(math.pow(NINF, 0.), 1.)\r
- self.assertEqual(math.pow(NINF, -0.), 1.)\r
- self.assertEqual(math.pow(NINF, -2.), 0.)\r
- self.assertEqual(math.pow(NINF, -2.3), 0.)\r
- self.assertEqual(math.pow(NINF, -3.), -0.)\r
- self.assertEqual(math.pow(NINF, NINF), 0.)\r
- self.assertTrue(math.isnan(math.pow(NINF, NAN)))\r
-\r
- # pow(-1, x)\r
- self.assertEqual(math.pow(-1., INF), 1.)\r
- self.assertEqual(math.pow(-1., 3.), -1.)\r
- self.assertRaises(ValueError, math.pow, -1., 2.3)\r
- self.assertEqual(math.pow(-1., 2.), 1.)\r
- self.assertEqual(math.pow(-1., 0.), 1.)\r
- self.assertEqual(math.pow(-1., -0.), 1.)\r
- self.assertEqual(math.pow(-1., -2.), 1.)\r
- self.assertRaises(ValueError, math.pow, -1., -2.3)\r
- self.assertEqual(math.pow(-1., -3.), -1.)\r
- self.assertEqual(math.pow(-1., NINF), 1.)\r
- self.assertTrue(math.isnan(math.pow(-1., NAN)))\r
-\r
- # pow(1, x)\r
- self.assertEqual(math.pow(1., INF), 1.)\r
- self.assertEqual(math.pow(1., 3.), 1.)\r
- self.assertEqual(math.pow(1., 2.3), 1.)\r
- self.assertEqual(math.pow(1., 2.), 1.)\r
- self.assertEqual(math.pow(1., 0.), 1.)\r
- self.assertEqual(math.pow(1., -0.), 1.)\r
- self.assertEqual(math.pow(1., -2.), 1.)\r
- self.assertEqual(math.pow(1., -2.3), 1.)\r
- self.assertEqual(math.pow(1., -3.), 1.)\r
- self.assertEqual(math.pow(1., NINF), 1.)\r
- self.assertEqual(math.pow(1., NAN), 1.)\r
-\r
- # pow(x, 0) should be 1 for any x\r
- self.assertEqual(math.pow(2.3, 0.), 1.)\r
- self.assertEqual(math.pow(-2.3, 0.), 1.)\r
- self.assertEqual(math.pow(NAN, 0.), 1.)\r
- self.assertEqual(math.pow(2.3, -0.), 1.)\r
- self.assertEqual(math.pow(-2.3, -0.), 1.)\r
- self.assertEqual(math.pow(NAN, -0.), 1.)\r
-\r
- # pow(x, y) is invalid if x is negative and y is not integral\r
- self.assertRaises(ValueError, math.pow, -1., 2.3)\r
- self.assertRaises(ValueError, math.pow, -15., -3.1)\r
-\r
- # pow(x, NINF)\r
- self.assertEqual(math.pow(1.9, NINF), 0.)\r
- self.assertEqual(math.pow(1.1, NINF), 0.)\r
- self.assertEqual(math.pow(0.9, NINF), INF)\r
- self.assertEqual(math.pow(0.1, NINF), INF)\r
- self.assertEqual(math.pow(-0.1, NINF), INF)\r
- self.assertEqual(math.pow(-0.9, NINF), INF)\r
- self.assertEqual(math.pow(-1.1, NINF), 0.)\r
- self.assertEqual(math.pow(-1.9, NINF), 0.)\r
-\r
- # pow(x, INF)\r
- self.assertEqual(math.pow(1.9, INF), INF)\r
- self.assertEqual(math.pow(1.1, INF), INF)\r
- self.assertEqual(math.pow(0.9, INF), 0.)\r
- self.assertEqual(math.pow(0.1, INF), 0.)\r
- self.assertEqual(math.pow(-0.1, INF), 0.)\r
- self.assertEqual(math.pow(-0.9, INF), 0.)\r
- self.assertEqual(math.pow(-1.1, INF), INF)\r
- self.assertEqual(math.pow(-1.9, INF), INF)\r
-\r
- # pow(x, y) should work for x negative, y an integer\r
- self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0)\r
- self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0)\r
- self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0)\r
- self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0)\r
- self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0)\r
- self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5)\r
- self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25)\r
- self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125)\r
- self.assertRaises(ValueError, math.pow, -2.0, -0.5)\r
- self.assertRaises(ValueError, math.pow, -2.0, 0.5)\r
-\r
- # the following tests have been commented out since they don't\r
- # really belong here: the implementation of ** for floats is\r
- # independent of the implementation of math.pow\r
- #self.assertEqual(1**NAN, 1)\r
- #self.assertEqual(1**INF, 1)\r
- #self.assertEqual(1**NINF, 1)\r
- #self.assertEqual(1**0, 1)\r
- #self.assertEqual(1.**NAN, 1)\r
- #self.assertEqual(1.**INF, 1)\r
- #self.assertEqual(1.**NINF, 1)\r
- #self.assertEqual(1.**0, 1)\r
-\r
- def testRadians(self):\r
- self.assertRaises(TypeError, math.radians)\r
- self.ftest('radians(180)', math.radians(180), math.pi)\r
- self.ftest('radians(90)', math.radians(90), math.pi/2)\r
- self.ftest('radians(-45)', math.radians(-45), -math.pi/4)\r
-\r
- def testSin(self):\r
- self.assertRaises(TypeError, math.sin)\r
- self.ftest('sin(0)', math.sin(0), 0)\r
- self.ftest('sin(pi/2)', math.sin(math.pi/2), 1)\r
- self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1)\r
- try:\r
- self.assertTrue(math.isnan(math.sin(INF)))\r
- self.assertTrue(math.isnan(math.sin(NINF)))\r
- except ValueError:\r
- self.assertRaises(ValueError, math.sin, INF)\r
- self.assertRaises(ValueError, math.sin, NINF)\r
- self.assertTrue(math.isnan(math.sin(NAN)))\r
-\r
- def testSinh(self):\r
- self.assertRaises(TypeError, math.sinh)\r
- self.ftest('sinh(0)', math.sinh(0), 0)\r
- self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1)\r
- self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0)\r
- self.assertEqual(math.sinh(INF), INF)\r
- self.assertEqual(math.sinh(NINF), NINF)\r
- self.assertTrue(math.isnan(math.sinh(NAN)))\r
-\r
- def testSqrt(self):\r
- self.assertRaises(TypeError, math.sqrt)\r
- self.ftest('sqrt(0)', math.sqrt(0), 0)\r
- self.ftest('sqrt(1)', math.sqrt(1), 1)\r
- self.ftest('sqrt(4)', math.sqrt(4), 2)\r
- self.assertEqual(math.sqrt(INF), INF)\r
- self.assertRaises(ValueError, math.sqrt, NINF)\r
- self.assertTrue(math.isnan(math.sqrt(NAN)))\r
-\r
- def testTan(self):\r
- self.assertRaises(TypeError, math.tan)\r
- self.ftest('tan(0)', math.tan(0), 0)\r
- self.ftest('tan(pi/4)', math.tan(math.pi/4), 1)\r
- self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1)\r
- try:\r
- self.assertTrue(math.isnan(math.tan(INF)))\r
- self.assertTrue(math.isnan(math.tan(NINF)))\r
- except:\r
- self.assertRaises(ValueError, math.tan, INF)\r
- self.assertRaises(ValueError, math.tan, NINF)\r
- self.assertTrue(math.isnan(math.tan(NAN)))\r
-\r
- def testTanh(self):\r
- self.assertRaises(TypeError, math.tanh)\r
- self.ftest('tanh(0)', math.tanh(0), 0)\r
- self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0)\r
- self.ftest('tanh(inf)', math.tanh(INF), 1)\r
- self.ftest('tanh(-inf)', math.tanh(NINF), -1)\r
- self.assertTrue(math.isnan(math.tanh(NAN)))\r
- # check that tanh(-0.) == -0. on IEEE 754 systems\r
- if float.__getformat__("double").startswith("IEEE"):\r
- self.assertEqual(math.tanh(-0.), -0.)\r
- self.assertEqual(math.copysign(1., math.tanh(-0.)),\r
- math.copysign(1., -0.))\r
-\r
- def test_trunc(self):\r
- self.assertEqual(math.trunc(1), 1)\r
- self.assertEqual(math.trunc(-1), -1)\r
- self.assertEqual(type(math.trunc(1)), int)\r
- self.assertEqual(type(math.trunc(1.5)), int)\r
- self.assertEqual(math.trunc(1.5), 1)\r
- self.assertEqual(math.trunc(-1.5), -1)\r
- self.assertEqual(math.trunc(1.999999), 1)\r
- self.assertEqual(math.trunc(-1.999999), -1)\r
- self.assertEqual(math.trunc(-0.999999), -0)\r
- self.assertEqual(math.trunc(-100.999), -100)\r
-\r
- class TestTrunc(object):\r
- def __trunc__(self):\r
- return 23\r
-\r
- class TestNoTrunc(object):\r
- pass\r
-\r
- self.assertEqual(math.trunc(TestTrunc()), 23)\r
-\r
- self.assertRaises(TypeError, math.trunc)\r
- self.assertRaises(TypeError, math.trunc, 1, 2)\r
- self.assertRaises((AttributeError, TypeError), math.trunc,\r
- TestNoTrunc())\r
-\r
- def testIsnan(self):\r
- self.assertTrue(math.isnan(float("nan")))\r
- self.assertTrue(math.isnan(float("inf")* 0.))\r
- self.assertFalse(math.isnan(float("inf")))\r
- self.assertFalse(math.isnan(0.))\r
- self.assertFalse(math.isnan(1.))\r
-\r
- def testIsinf(self):\r
- self.assertTrue(math.isinf(float("inf")))\r
- self.assertTrue(math.isinf(float("-inf")))\r
- self.assertTrue(math.isinf(1E400))\r
- self.assertTrue(math.isinf(-1E400))\r
- self.assertFalse(math.isinf(float("nan")))\r
- self.assertFalse(math.isinf(0.))\r
- self.assertFalse(math.isinf(1.))\r
-\r
- # RED_FLAG 16-Oct-2000 Tim\r
- # While 2.0 is more consistent about exceptions than previous releases, it\r
- # still fails this part of the test on some platforms. For now, we only\r
- # *run* test_exceptions() in verbose mode, so that this isn't normally\r
- # tested.\r
-\r
- if verbose:\r
- def test_exceptions(self):\r
- try:\r
- x = math.exp(-1000000000)\r
- except:\r
- # mathmodule.c is failing to weed out underflows from libm, or\r
- # we've got an fp format with huge dynamic range\r
- self.fail("underflowing exp() should not have raised "\r
- "an exception")\r
- if x != 0:\r
- self.fail("underflowing exp() should have returned 0")\r
-\r
- # If this fails, probably using a strict IEEE-754 conforming libm, and x\r
- # is +Inf afterwards. But Python wants overflows detected by default.\r
- try:\r
- x = math.exp(1000000000)\r
- except OverflowError:\r
- pass\r
- else:\r
- self.fail("overflowing exp() didn't trigger OverflowError")\r
-\r
- # If this fails, it could be a puzzle. One odd possibility is that\r
- # mathmodule.c's macros are getting confused while comparing\r
- # Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE\r
- # as a result (and so raising OverflowError instead).\r
- try:\r
- x = math.sqrt(-1.0)\r
- except ValueError:\r
- pass\r
- else:\r
- self.fail("sqrt(-1) didn't raise ValueError")\r
-\r
- @requires_IEEE_754\r
- def test_testfile(self):\r
- for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file):\r
- # Skip if either the input or result is complex, or if\r
- # flags is nonempty\r
- if ai != 0. or ei != 0. or flags:\r
- continue\r
- if fn in ['rect', 'polar']:\r
- # no real versions of rect, polar\r
- continue\r
- func = getattr(math, fn)\r
- try:\r
- result = func(ar)\r
- except ValueError:\r
- message = ("Unexpected ValueError in " +\r
- "test %s:%s(%r)\n" % (id, fn, ar))\r
- self.fail(message)\r
- except OverflowError:\r
- message = ("Unexpected OverflowError in " +\r
- "test %s:%s(%r)\n" % (id, fn, ar))\r
- self.fail(message)\r
- self.ftest("%s:%s(%r)" % (id, fn, ar), result, er)\r
-\r
- @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),\r
- "test requires IEEE 754 doubles")\r
- def test_mtestfile(self):\r
- ALLOWED_ERROR = 20 # permitted error, in ulps\r
- fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}"\r
-\r
- failures = []\r
- for id, fn, arg, expected, flags in parse_mtestfile(math_testcases):\r
- func = getattr(math, fn)\r
-\r
- if 'invalid' in flags or 'divide-by-zero' in flags:\r
- expected = 'ValueError'\r
- elif 'overflow' in flags:\r
- expected = 'OverflowError'\r
-\r
- try:\r
- got = func(arg)\r
- except ValueError:\r
- got = 'ValueError'\r
- except OverflowError:\r
- got = 'OverflowError'\r
-\r
- accuracy_failure = None\r
- if isinstance(got, float) and isinstance(expected, float):\r
- if math.isnan(expected) and math.isnan(got):\r
- continue\r
- if not math.isnan(expected) and not math.isnan(got):\r
- if fn == 'lgamma':\r
- # we use a weaker accuracy test for lgamma;\r
- # lgamma only achieves an absolute error of\r
- # a few multiples of the machine accuracy, in\r
- # general.\r
- accuracy_failure = acc_check(expected, got,\r
- rel_err = 5e-15,\r
- abs_err = 5e-15)\r
- elif fn == 'erfc':\r
- # erfc has less-than-ideal accuracy for large\r
- # arguments (x ~ 25 or so), mainly due to the\r
- # error involved in computing exp(-x*x).\r
- #\r
- # XXX Would be better to weaken this test only\r
- # for large x, instead of for all x.\r
- accuracy_failure = ulps_check(expected, got, 2000)\r
-\r
- else:\r
- accuracy_failure = ulps_check(expected, got, 20)\r
- if accuracy_failure is None:\r
- continue\r
-\r
- if isinstance(got, str) and isinstance(expected, str):\r
- if got == expected:\r
- continue\r
-\r
- fail_msg = fail_fmt.format(id, fn, arg, expected, got)\r
- if accuracy_failure is not None:\r
- fail_msg += ' ({})'.format(accuracy_failure)\r
- failures.append(fail_msg)\r
-\r
- if failures:\r
- self.fail('Failures in test_mtestfile:\n ' +\r
- '\n '.join(failures))\r
-\r
-\r
-def test_main():\r
- from doctest import DocFileSuite\r
- suite = unittest.TestSuite()\r
- suite.addTest(unittest.makeSuite(MathTests))\r
- suite.addTest(DocFileSuite("ieee754.txt"))\r
- run_unittest(suite)\r
-\r
-if __name__ == '__main__':\r
- test_main()\r
projects / mirror_edk2.git / blobdiff