diff options
Diffstat (limited to 'Lib/test/test_math.py')
| -rw-r--r-- | Lib/test/test_math.py | 326 |
1 files changed, 258 insertions, 68 deletions
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py index 9a87d5d307..dddc889375 100644 --- a/Lib/test/test_math.py +++ b/Lib/test/test_math.py @@ -1,12 +1,14 @@ # Python test set -- math module # XXXX Should not do tests around zero only -from test.support import run_unittest, verbose +from test.support import run_unittest, verbose, requires_IEEE_754 import unittest import math import os import sys import random +import struct +import sysconfig eps = 1E-05 NAN = float('nan') @@ -24,8 +26,130 @@ if __name__ == '__main__': 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) + +# Here's a pure Python version of the math.factorial algorithm, for +# documentation and comparison purposes. +# +# Formula: +# +# factorial(n) = factorial_odd_part(n) << (n - count_set_bits(n)) +# +# where +# +# factorial_odd_part(n) = product_{i >= 0} product_{0 < j <= n >> i; j odd} j +# +# The outer product above is an infinite product, but once i >= n.bit_length, +# (n >> i) < 1 and the corresponding term of the product is empty. So only the +# finitely many terms for 0 <= i < n.bit_length() contribute anything. +# +# We iterate downwards from i == n.bit_length() - 1 to i == 0. The inner +# product in the formula above starts at 1 for i == n.bit_length(); for each i +# < n.bit_length() we get the inner product for i from that for i + 1 by +# multiplying by all j in {n >> i+1 < j <= n >> i; j odd}. In Python terms, +# this set is range((n >> i+1) + 1 | 1, (n >> i) + 1 | 1, 2). + +def count_set_bits(n): + """Number of '1' bits in binary expansion of a nonnnegative integer.""" + return 1 + count_set_bits(n & n - 1) if n else 0 + +def partial_product(start, stop): + """Product of integers in range(start, stop, 2), computed recursively. + start and stop should both be odd, with start <= stop. + + """ + numfactors = (stop - start) >> 1 + if not numfactors: + return 1 + elif numfactors == 1: + return start + else: + mid = (start + numfactors) | 1 + return partial_product(start, mid) * partial_product(mid, stop) + +def py_factorial(n): + """Factorial of nonnegative integer n, via "Binary Split Factorial Formula" + described at http://www.luschny.de/math/factorial/binarysplitfact.html + + """ + inner = outer = 1 + for i in reversed(range(n.bit_length())): + inner *= partial_product((n >> i + 1) + 1 | 1, (n >> i) + 1 | 1) + outer *= inner + return outer << (n - count_set_bits(n)) + +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 @@ -209,39 +333,39 @@ class MathTests(unittest.TestCase): self.assertRaises(TypeError, math.ceil, t) self.assertRaises(TypeError, math.ceil, t, 0) - if float.__getformat__("double").startswith("IEEE"): - 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.) + @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) @@ -287,18 +411,19 @@ class MathTests(unittest.TestCase): 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 = list(range(10)) + [50, 100, 500] - random.shuffle(values) - for x in values: - for cast in (int, float): - self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x))) + self.assertEqual(math.factorial(0), 1) + self.assertEqual(math.factorial(0.0), 1) + total = 1 + for i in range(1, 1000): + total *= i + self.assertEqual(math.factorial(i), total) + self.assertEqual(math.factorial(float(i)), total) + self.assertEqual(math.factorial(i), py_factorial(i)) self.assertRaises(ValueError, math.factorial, -1) + self.assertRaises(ValueError, math.factorial, -1.0) self.assertRaises(ValueError, math.factorial, math.pi) + self.assertRaises(OverflowError, math.factorial, sys.maxsize+1) + self.assertRaises(OverflowError, math.factorial, 10e100) def testFloor(self): self.assertRaises(TypeError, math.floor) @@ -370,8 +495,7 @@ class MathTests(unittest.TestCase): self.assertEqual(math.frexp(NINF)[0], NINF) self.assertTrue(math.isnan(math.frexp(NAN)[0])) - @unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), - "test requires IEEE 754 doubles") + @requires_IEEE_754 @unittest.skipIf(HAVE_DOUBLE_ROUNDING, "fsum is not exact on machines with double rounding") def testFsum(self): @@ -513,21 +637,17 @@ class MathTests(unittest.TestCase): 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.ftest('log(10**1000)', math.log(10**1000), + 2302.5850929940457) + self.assertRaises(ValueError, math.log, -1.5) + self.assertRaises(ValueError, math.log, -10**1000) self.assertRaises(ValueError, math.log, NINF) + self.assertEqual(math.log(INF), INF) 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): @@ -535,8 +655,11 @@ class MathTests(unittest.TestCase): 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.ftest('log10(10**1000)', math.log10(10**1000), 1000.0) + self.assertRaises(ValueError, math.log10, -1.5) + self.assertRaises(ValueError, math.log10, -10**1000) self.assertRaises(ValueError, math.log10, NINF) + self.assertEqual(math.log(INF), INF) self.assertTrue(math.isnan(math.log10(NAN))) def testModf(self): @@ -764,11 +887,15 @@ class MathTests(unittest.TestCase): self.ftest('tanh(inf)', math.tanh(INF), 1) self.ftest('tanh(-inf)', math.tanh(NINF), -1) self.assertTrue(math.isnan(math.tanh(NAN))) + + @requires_IEEE_754 + @unittest.skipIf(sysconfig.get_config_var('TANH_PRESERVES_ZERO_SIGN') == 0, + "system tanh() function doesn't copy the sign") + def testTanhSign(self): # 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.)) + 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) @@ -795,12 +922,14 @@ class MathTests(unittest.TestCase): self.assertRaises(TypeError, math.trunc, 1, 2) self.assertRaises(TypeError, math.trunc, TestNoTrunc()) - # XXX Doesn't work because the method is looked up on - # the type only. - #t = TestNoTrunc() - #t.__trunc__ = lambda *args: args - #self.assertEqual((), math.trunc(t)) - #self.assertRaises(TypeError, math.trunc, t, 0) + def testIsfinite(self): + self.assertTrue(math.isfinite(0.0)) + self.assertTrue(math.isfinite(-0.0)) + self.assertTrue(math.isfinite(1.0)) + self.assertTrue(math.isfinite(-1.0)) + self.assertFalse(math.isfinite(float("nan"))) + self.assertFalse(math.isfinite(float("inf"))) + self.assertFalse(math.isfinite(float("-inf"))) def testIsnan(self): self.assertTrue(math.isnan(float("nan"))) @@ -856,9 +985,8 @@ class MathTests(unittest.TestCase): else: self.fail("sqrt(-1) didn't raise ValueError") + @requires_IEEE_754 def test_testfile(self): - if not float.__getformat__("double").startswith("IEEE"): - return for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file): # Skip if either the input or result is complex, or if # flags is nonempty @@ -880,6 +1008,68 @@ class MathTests(unittest.TestCase): self.fail(message) self.ftest("%s:%s(%r)" % (id, fn, ar), result, er) + @requires_IEEE_754 + 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() |