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✏️ test_math.py
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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))) # Log values should match for int and long (issue #18739). for n in range(1, 1000): self.assertEqual(math.log(n), math.log(long(n))) def testLog1p(self): self.assertRaises(TypeError, math.log1p) self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1) self.ftest('log1p(0)', math.log1p(0), 0) self.ftest('log1p(e-1)', math.log1p(math.e-1), 1) self.ftest('log1p(1)', math.log1p(1), math.log(2)) self.assertEqual(math.log1p(INF), INF) self.assertRaises(ValueError, math.log1p, NINF) self.assertTrue(math.isnan(math.log1p(NAN))) n= 2**90 self.assertAlmostEqual(math.log1p(n), 62.383246250395075) self.assertAlmostEqual(math.log1p(n), math.log1p(float(n))) def 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))) # Log values should match for int and long (issue #18739). for n in range(1, 1000): self.assertEqual(math.log10(n), math.log10(long(n))) 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. @unittest.skipUnless(verbose, 'requires verbose mode') 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()
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