| # Python test set -- math module |
| # XXXX Should not do tests around zero only |
| |
| from test.support import run_unittest, verbose, requires_IEEE_754 |
| from test import support |
| import unittest |
| import math |
| import os |
| import platform |
| import struct |
| import sys |
| import sysconfig |
| |
| eps = 1E-05 |
| NAN = float('nan') |
| INF = float('inf') |
| NINF = float('-inf') |
| FLOAT_MAX = sys.float_info.max |
| |
| # 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 native doubles are represented in IEEE 754 binary64 format. |
| |
| Note: 0.0 and -0.0 are converted to 0 and -1, respectively. |
| """ |
| n = struct.unpack('<q', struct.pack('<d', x))[0] |
| if n < 0: |
| n = ~(n+2**63) |
| return n |
| |
| |
| def ulp(x): |
| """Return the value of the least significant bit of a |
| float x, such that the first float bigger than x is x+ulp(x). |
| Then, given an expected result x and a tolerance of n ulps, |
| the result y should be such that abs(y-x) <= n * ulp(x). |
| The results from this function will only make sense on platforms |
| where native doubles are represented in IEEE 754 binary64 format. |
| """ |
| x = abs(float(x)) |
| if math.isnan(x) or math.isinf(x): |
| return x |
| |
| # Find next float up from x. |
| n = struct.unpack('<q', struct.pack('<d', x))[0] |
| x_next = struct.unpack('<d', struct.pack('<q', n + 1))[0] |
| if math.isinf(x_next): |
| # Corner case: x was the largest finite float. Then it's |
| # not an exact power of two, so we can take the difference |
| # between x and the previous float. |
| x_prev = struct.unpack('<d', struct.pack('<q', n - 1))[0] |
| return x - x_prev |
| else: |
| return x_next - x |
| |
| # 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 ulp_abs_check(expected, got, ulp_tol, abs_tol): |
| """Given finite floats `expected` and `got`, check that they're |
| approximately equal to within the given number of ulps or the |
| given absolute tolerance, whichever is bigger. |
| |
| Returns None on success and an error message on failure. |
| """ |
| ulp_error = abs(to_ulps(expected) - to_ulps(got)) |
| abs_error = abs(expected - got) |
| |
| # Succeed if either abs_error <= abs_tol or ulp_error <= ulp_tol. |
| if abs_error <= abs_tol or ulp_error <= ulp_tol: |
| return None |
| else: |
| fmt = ("error = {:.3g} ({:d} ulps); " |
| "permitted error = {:.3g} or {:d} ulps") |
| return fmt.format(abs_error, ulp_error, abs_tol, ulp_tol) |
| |
| 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) |
| |
| |
| def result_check(expected, got, ulp_tol=5, abs_tol=0.0): |
| # Common logic of MathTests.(ftest, test_testcases, test_mtestcases) |
| """Compare arguments expected and got, as floats, if either |
| is a float, using a tolerance expressed in multiples of |
| ulp(expected) or absolutely (if given and greater). |
| |
| As a convenience, when neither argument is a float, and for |
| non-finite floats, exact equality is demanded. Also, nan==nan |
| as far as this function is concerned. |
| |
| Returns None on success and an error message on failure. |
| """ |
| |
| # Check exactly equal (applies also to strings representing exceptions) |
| if got == expected: |
| return None |
| |
| failure = "not equal" |
| |
| # Turn mixed float and int comparison (e.g. floor()) to all-float |
| if isinstance(expected, float) and isinstance(got, int): |
| got = float(got) |
| elif isinstance(got, float) and isinstance(expected, int): |
| expected = float(expected) |
| |
| if isinstance(expected, float) and isinstance(got, float): |
| if math.isnan(expected) and math.isnan(got): |
| # Pass, since both nan |
| failure = None |
| elif math.isinf(expected) or math.isinf(got): |
| # We already know they're not equal, drop through to failure |
| pass |
| else: |
| # Both are finite floats (now). Are they close enough? |
| failure = ulp_abs_check(expected, got, ulp_tol, abs_tol) |
| |
| # arguments are not equal, and if numeric, are too far apart |
| if failure is not None: |
| fail_fmt = "expected {!r}, got {!r}" |
| fail_msg = fail_fmt.format(expected, got) |
| fail_msg += ' ({})'.format(failure) |
| return fail_msg |
| else: |
| return None |
| |
| # Class providing an __index__ method. |
| class MyIndexable(object): |
| def __init__(self, value): |
| self.value = value |
| |
| def __index__(self): |
| return self.value |
| |
| class MathTests(unittest.TestCase): |
| |
| def ftest(self, name, got, expected, ulp_tol=5, abs_tol=0.0): |
| """Compare arguments expected and got, as floats, if either |
| is a float, using a tolerance expressed in multiples of |
| ulp(expected) or absolutely, whichever is greater. |
| |
| As a convenience, when neither argument is a float, and for |
| non-finite floats, exact equality is demanded. Also, nan==nan |
| in this function. |
| """ |
| failure = result_check(expected, got, ulp_tol, abs_tol) |
| if failure is not None: |
| self.fail("{}: {}".format(name, failure)) |
| |
| def testConstants(self): |
| # Ref: Abramowitz & Stegun (Dover, 1965) |
| self.ftest('pi', math.pi, 3.141592653589793238462643) |
| self.ftest('e', math.e, 2.718281828459045235360287) |
| self.assertEqual(math.tau, 2*math.pi) |
| |
| 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.assertRaises(ValueError, math.acos, 1 + eps) |
| self.assertRaises(ValueError, math.acos, -1 - eps) |
| 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.assertRaises(ValueError, math.asin, 1 + eps) |
| self.assertRaises(ValueError, math.asin, -1 - eps) |
| 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) |
| self.assertEqual(int, type(math.ceil(0.5))) |
| 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: |
| def __ceil__(self): |
| return 42 |
| class TestNoCeil: |
| 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, abs_tol=ulp(1)) |
| self.ftest('cos(0)', math.cos(0), 1) |
| self.ftest('cos(pi/2)', math.cos(math.pi/2), 0, abs_tol=ulp(1)) |
| 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) |
| self.ftest('degrees(0)', math.degrees(0), 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))) |
| self.assertRaises(OverflowError, math.exp, 1000000) |
| |
| 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): |
| 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, -10**100) |
| self.assertRaises(ValueError, math.factorial, -1e100) |
| self.assertRaises(ValueError, math.factorial, math.pi) |
| |
| # Other implementations may place different upper bounds. |
| @support.cpython_only |
| def testFactorialHugeInputs(self): |
| # Currently raises ValueError for inputs that are too large |
| # to fit into a C long. |
| self.assertRaises(OverflowError, math.factorial, 10**100) |
| self.assertRaises(OverflowError, math.factorial, 1e100) |
| |
| def testFloor(self): |
| self.assertRaises(TypeError, math.floor) |
| self.assertEqual(int, type(math.floor(0.5))) |
| 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: |
| def __floor__(self): |
| return 42 |
| class TestNoFloor: |
| 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), 0.0) |
| self.ftest('fmod(10, 0.5)', math.fmod(10, 0.5), 0.0) |
| self.ftest('fmod(10, 1.5)', math.fmod(10, 1.5), 1.0) |
| self.ftest('fmod(-10, 1)', math.fmod(-10, 1), -0.0) |
| self.ftest('fmod(-10, 0.5)', math.fmod(-10, 0.5), -0.0) |
| self.ftest('fmod(-10, 1.5)', math.fmod(-10, 1.5), -1.0) |
| 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, result, expected)) |
| |
| 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 range(1000): |
| vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10 |
| s = 0 |
| for i in range(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 testGcd(self): |
| gcd = math.gcd |
| self.assertEqual(gcd(0, 0), 0) |
| self.assertEqual(gcd(1, 0), 1) |
| self.assertEqual(gcd(-1, 0), 1) |
| self.assertEqual(gcd(0, 1), 1) |
| self.assertEqual(gcd(0, -1), 1) |
| self.assertEqual(gcd(7, 1), 1) |
| self.assertEqual(gcd(7, -1), 1) |
| self.assertEqual(gcd(-23, 15), 1) |
| self.assertEqual(gcd(120, 84), 12) |
| self.assertEqual(gcd(84, -120), 12) |
| self.assertEqual(gcd(1216342683557601535506311712, |
| 436522681849110124616458784), 32) |
| c = 652560 |
| x = 434610456570399902378880679233098819019853229470286994367836600566 |
| y = 1064502245825115327754847244914921553977 |
| a = x * c |
| b = y * c |
| self.assertEqual(gcd(a, b), c) |
| self.assertEqual(gcd(b, a), c) |
| self.assertEqual(gcd(-a, b), c) |
| self.assertEqual(gcd(b, -a), c) |
| self.assertEqual(gcd(a, -b), c) |
| self.assertEqual(gcd(-b, a), c) |
| self.assertEqual(gcd(-a, -b), c) |
| self.assertEqual(gcd(-b, -a), c) |
| c = 576559230871654959816130551884856912003141446781646602790216406874 |
| a = x * c |
| b = y * c |
| self.assertEqual(gcd(a, b), c) |
| self.assertEqual(gcd(b, a), c) |
| self.assertEqual(gcd(-a, b), c) |
| self.assertEqual(gcd(b, -a), c) |
| self.assertEqual(gcd(a, -b), c) |
| self.assertEqual(gcd(-b, a), c) |
| self.assertEqual(gcd(-a, -b), c) |
| self.assertEqual(gcd(-b, -a), c) |
| |
| self.assertRaises(TypeError, gcd, 120.0, 84) |
| self.assertRaises(TypeError, gcd, 120, 84.0) |
| self.assertEqual(gcd(MyIndexable(120), MyIndexable(84)), 12) |
| |
| 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.assertRaises(OverflowError, math.hypot, FLOAT_MAX, FLOAT_MAX) |
| 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, 10**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.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) |
| for n in [2, 2**90, 2**300]: |
| self.assertAlmostEqual(math.log1p(n), math.log1p(float(n))) |
| self.assertRaises(ValueError, math.log1p, -1) |
| self.assertEqual(math.log1p(INF), INF) |
| |
| @requires_IEEE_754 |
| def testLog2(self): |
| self.assertRaises(TypeError, math.log2) |
| |
| # Check some integer values |
| self.assertEqual(math.log2(1), 0.0) |
| self.assertEqual(math.log2(2), 1.0) |
| self.assertEqual(math.log2(4), 2.0) |
| |
| # Large integer values |
| self.assertEqual(math.log2(2**1023), 1023.0) |
| self.assertEqual(math.log2(2**1024), 1024.0) |
| self.assertEqual(math.log2(2**2000), 2000.0) |
| |
| self.assertRaises(ValueError, math.log2, -1.5) |
| self.assertRaises(ValueError, math.log2, NINF) |
| self.assertTrue(math.isnan(math.log2(NAN))) |
| |
| @requires_IEEE_754 |
| # log2() is not accurate enough on Mac OS X Tiger (10.4) |
| @support.requires_mac_ver(10, 5) |
| def testLog2Exact(self): |
| # Check that we get exact equality for log2 of powers of 2. |
| actual = [math.log2(math.ldexp(1.0, n)) for n in range(-1074, 1024)] |
| expected = [float(n) for n in range(-1074, 1024)] |
| self.assertEqual(actual, expected) |
| |
| 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.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): |
| 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, result, expected)) |
| |
| 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) |
| self.ftest('radians(0)', math.radians(0), 0) |
| |
| 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, -1) |
| 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, |
| abs_tol=ulp(1)) |
| 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 |
| 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(TypeError, math.trunc, TestNoTrunc()) |
| |
| 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"))) |
| 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.)) |
| |
| @requires_IEEE_754 |
| def test_nan_constant(self): |
| self.assertTrue(math.isnan(math.nan)) |
| |
| @requires_IEEE_754 |
| def test_inf_constant(self): |
| self.assertTrue(math.isinf(math.inf)) |
| self.assertGreater(math.inf, 0.0) |
| self.assertEqual(math.inf, float("inf")) |
| self.assertEqual(-math.inf, float("-inf")) |
| |
| # 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): |
| # Some tests need to be skipped on ancient OS X versions. |
| # See issue #27953. |
| SKIP_ON_TIGER = {'tan0064'} |
| |
| osx_version = None |
| if sys.platform == 'darwin': |
| version_txt = platform.mac_ver()[0] |
| try: |
| osx_version = tuple(map(int, version_txt.split('.'))) |
| except ValueError: |
| pass |
| |
| fail_fmt = "{}: {}({!r}): {}" |
| |
| failures = [] |
| for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file): |
| # Skip if either the input or result is complex |
| if ai != 0.0 or ei != 0.0: |
| continue |
| if fn in ['rect', 'polar']: |
| # no real versions of rect, polar |
| continue |
| # Skip certain tests on OS X 10.4. |
| if osx_version is not None and osx_version < (10, 5): |
| if id in SKIP_ON_TIGER: |
| continue |
| |
| func = getattr(math, fn) |
| |
| if 'invalid' in flags or 'divide-by-zero' in flags: |
| er = 'ValueError' |
| elif 'overflow' in flags: |
| er = 'OverflowError' |
| |
| try: |
| result = func(ar) |
| except ValueError: |
| result = 'ValueError' |
| except OverflowError: |
| result = 'OverflowError' |
| |
| # Default tolerances |
| ulp_tol, abs_tol = 5, 0.0 |
| |
| failure = result_check(er, result, ulp_tol, abs_tol) |
| if failure is None: |
| continue |
| |
| msg = fail_fmt.format(id, fn, ar, failure) |
| failures.append(msg) |
| |
| if failures: |
| self.fail('Failures in test_testfile:\n ' + |
| '\n '.join(failures)) |
| |
| @requires_IEEE_754 |
| def test_mtestfile(self): |
| fail_fmt = "{}: {}({!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' |
| |
| # Default tolerances |
| ulp_tol, abs_tol = 5, 0.0 |
| |
| # Exceptions to the defaults |
| if fn == 'gamma': |
| # Experimental results on one platform gave |
| # an accuracy of <= 10 ulps across the entire float |
| # domain. We weaken that to require 20 ulp accuracy. |
| ulp_tol = 20 |
| |
| elif 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. |
| abs_tol = 1e-15 |
| |
| elif fn == 'erfc' and arg >= 0.0: |
| # erfc has less-than-ideal accuracy for large |
| # arguments (x ~ 25 or so), mainly due to the |
| # error involved in computing exp(-x*x). |
| # |
| # Observed between CPython and mpmath at 25 dp: |
| # x < 0 : err <= 2 ulp |
| # 0 <= x < 1 : err <= 10 ulp |
| # 1 <= x < 10 : err <= 100 ulp |
| # 10 <= x < 20 : err <= 300 ulp |
| # 20 <= x : < 600 ulp |
| # |
| if arg < 1.0: |
| ulp_tol = 10 |
| elif arg < 10.0: |
| ulp_tol = 100 |
| else: |
| ulp_tol = 1000 |
| |
| failure = result_check(expected, got, ulp_tol, abs_tol) |
| if failure is None: |
| continue |
| |
| msg = fail_fmt.format(id, fn, arg, failure) |
| failures.append(msg) |
| |
| if failures: |
| self.fail('Failures in test_mtestfile:\n ' + |
| '\n '.join(failures)) |
| |
| |
| class IsCloseTests(unittest.TestCase): |
| isclose = math.isclose # subclasses should override this |
| |
| def assertIsClose(self, a, b, *args, **kwargs): |
| self.assertTrue(self.isclose(a, b, *args, **kwargs), |
| msg="%s and %s should be close!" % (a, b)) |
| |
| def assertIsNotClose(self, a, b, *args, **kwargs): |
| self.assertFalse(self.isclose(a, b, *args, **kwargs), |
| msg="%s and %s should not be close!" % (a, b)) |
| |
| def assertAllClose(self, examples, *args, **kwargs): |
| for a, b in examples: |
| self.assertIsClose(a, b, *args, **kwargs) |
| |
| def assertAllNotClose(self, examples, *args, **kwargs): |
| for a, b in examples: |
| self.assertIsNotClose(a, b, *args, **kwargs) |
| |
| def test_negative_tolerances(self): |
| # ValueError should be raised if either tolerance is less than zero |
| with self.assertRaises(ValueError): |
| self.assertIsClose(1, 1, rel_tol=-1e-100) |
| with self.assertRaises(ValueError): |
| self.assertIsClose(1, 1, rel_tol=1e-100, abs_tol=-1e10) |
| |
| def test_identical(self): |
| # identical values must test as close |
| identical_examples = [(2.0, 2.0), |
| (0.1e200, 0.1e200), |
| (1.123e-300, 1.123e-300), |
| (12345, 12345.0), |
| (0.0, -0.0), |
| (345678, 345678)] |
| self.assertAllClose(identical_examples, rel_tol=0.0, abs_tol=0.0) |
| |
| def test_eight_decimal_places(self): |
| # examples that are close to 1e-8, but not 1e-9 |
| eight_decimal_places_examples = [(1e8, 1e8 + 1), |
| (-1e-8, -1.000000009e-8), |
| (1.12345678, 1.12345679)] |
| self.assertAllClose(eight_decimal_places_examples, rel_tol=1e-8) |
| self.assertAllNotClose(eight_decimal_places_examples, rel_tol=1e-9) |
| |
| def test_near_zero(self): |
| # values close to zero |
| near_zero_examples = [(1e-9, 0.0), |
| (-1e-9, 0.0), |
| (-1e-150, 0.0)] |
| # these should not be close to any rel_tol |
| self.assertAllNotClose(near_zero_examples, rel_tol=0.9) |
| # these should be close to abs_tol=1e-8 |
| self.assertAllClose(near_zero_examples, abs_tol=1e-8) |
| |
| def test_identical_infinite(self): |
| # these are close regardless of tolerance -- i.e. they are equal |
| self.assertIsClose(INF, INF) |
| self.assertIsClose(INF, INF, abs_tol=0.0) |
| self.assertIsClose(NINF, NINF) |
| self.assertIsClose(NINF, NINF, abs_tol=0.0) |
| |
| def test_inf_ninf_nan(self): |
| # these should never be close (following IEEE 754 rules for equality) |
| not_close_examples = [(NAN, NAN), |
| (NAN, 1e-100), |
| (1e-100, NAN), |
| (INF, NAN), |
| (NAN, INF), |
| (INF, NINF), |
| (INF, 1.0), |
| (1.0, INF), |
| (INF, 1e308), |
| (1e308, INF)] |
| # use largest reasonable tolerance |
| self.assertAllNotClose(not_close_examples, abs_tol=0.999999999999999) |
| |
| def test_zero_tolerance(self): |
| # test with zero tolerance |
| zero_tolerance_close_examples = [(1.0, 1.0), |
| (-3.4, -3.4), |
| (-1e-300, -1e-300)] |
| self.assertAllClose(zero_tolerance_close_examples, rel_tol=0.0) |
| |
| zero_tolerance_not_close_examples = [(1.0, 1.000000000000001), |
| (0.99999999999999, 1.0), |
| (1.0e200, .999999999999999e200)] |
| self.assertAllNotClose(zero_tolerance_not_close_examples, rel_tol=0.0) |
| |
| def test_asymmetry(self): |
| # test the asymmetry example from PEP 485 |
| self.assertAllClose([(9, 10), (10, 9)], rel_tol=0.1) |
| |
| def test_integers(self): |
| # test with integer values |
| integer_examples = [(100000001, 100000000), |
| (123456789, 123456788)] |
| |
| self.assertAllClose(integer_examples, rel_tol=1e-8) |
| self.assertAllNotClose(integer_examples, rel_tol=1e-9) |
| |
| def test_decimals(self): |
| # test with Decimal values |
| from decimal import Decimal |
| |
| decimal_examples = [(Decimal('1.00000001'), Decimal('1.0')), |
| (Decimal('1.00000001e-20'), Decimal('1.0e-20')), |
| (Decimal('1.00000001e-100'), Decimal('1.0e-100')), |
| (Decimal('1.00000001e20'), Decimal('1.0e20'))] |
| self.assertAllClose(decimal_examples, rel_tol=1e-8) |
| self.assertAllNotClose(decimal_examples, rel_tol=1e-9) |
| |
| def test_fractions(self): |
| # test with Fraction values |
| from fractions import Fraction |
| |
| fraction_examples = [ |
| (Fraction(1, 100000000) + 1, Fraction(1)), |
| (Fraction(100000001), Fraction(100000000)), |
| (Fraction(10**8 + 1, 10**28), Fraction(1, 10**20))] |
| self.assertAllClose(fraction_examples, rel_tol=1e-8) |
| self.assertAllNotClose(fraction_examples, rel_tol=1e-9) |
| |
| |
| def test_main(): |
| from doctest import DocFileSuite |
| suite = unittest.TestSuite() |
| suite.addTest(unittest.makeSuite(MathTests)) |
| suite.addTest(unittest.makeSuite(IsCloseTests)) |
| suite.addTest(DocFileSuite("ieee754.txt")) |
| run_unittest(suite) |
| |
| if __name__ == '__main__': |
| test_main() |
