diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py new file mode 100644 index 0000000000..4c3cdfbb75 --- /dev/null +++ b/Lib/test/test_math.py @@ -0,0 +1,2190 @@ + +# Python test set -- math module +# XXXX Should not do tests around zero only + +from test.support import run_unittest, verbose#, requires_IEEE_754 # TODO: RUSTPYTHON, commented due to import error +from test import support +import unittest +import itertools +import decimal +import math +import os +import platform +import random +import struct +import sys + + +eps = 1E-05 +NAN = float('nan') +INF = float('inf') +NINF = float('-inf') + +# TODO RustPython: float_info is so far not supported -> hard code for the moment +# FLOAT_MAX = sys.float_info.max +# FLOAT_MIN = sys.float_info.min +FLOAT_MAX = 1.7976931348623157e+308 +FLOAT_MIN = 2.2250738585072014e-308 + +# 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('= 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 FloatLike: + def __init__(self, value): + self.value = value + + def __float__(self): + return self.value + +class IntSubclass(int): + pass + +# 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) + + @unittest.skip('RustPython') + 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))) + + @unittest.skip('RustPython') + 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))) + + @unittest.skip('RustPython') + 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))) + + @unittest.skip('RustPython') + 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))) + + @unittest.skip('RustPython') + def testCeil(self): + self.assertRaises(TypeError, math.ceil) + self.assertEqual(int, type(math.ceil(0.5))) + self.assertEqual(math.ceil(0.5), 1) + self.assertEqual(math.ceil(1.0), 1) + self.assertEqual(math.ceil(1.5), 2) + self.assertEqual(math.ceil(-0.5), 0) + self.assertEqual(math.ceil(-1.0), -1) + self.assertEqual(math.ceil(-1.5), -1) + self.assertEqual(math.ceil(0.0), 0) + self.assertEqual(math.ceil(-0.0), 0) + #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 FloatCeil(float): + def __ceil__(self): + return 42 + class TestNoCeil: + pass + self.assertEqual(math.ceil(TestCeil()), 42) + self.assertEqual(math.ceil(FloatCeil()), 42) + self.assertEqual(math.ceil(FloatLike(42.5)), 43) + 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) + + # TODO Rustpython + # @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.) + + @unittest.skip('RustPython') + def testCos(self): + self.assertRaises(TypeError, math.cos) + self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0, abs_tol=math.ulp(1)) + self.ftest('cos(0)', math.cos(0), 1) + self.ftest('cos(pi/2)', math.cos(math.pi/2), 0, abs_tol=math.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))) + + @unittest.skipIf(sys.platform == 'win32' and platform.machine() in ('ARM', 'ARM64'), + "Windows UCRT is off by 2 ULP this test requires accuracy within 1 ULP") + 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) + + @unittest.skip('TODO RustPython') + 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) + total = 1 + for i in range(1, 1000): + total *= i + self.assertEqual(math.factorial(i), total) + self.assertEqual(math.factorial(i), py_factorial(i)) + self.assertRaises(ValueError, math.factorial, -1) + self.assertRaises(ValueError, math.factorial, -10**100) + + @unittest.skip('RustPython') + def testFactorialNonIntegers(self): + with self.assertWarns(DeprecationWarning): + self.assertEqual(math.factorial(5.0), 120) + with self.assertWarns(DeprecationWarning): + self.assertRaises(ValueError, math.factorial, 5.2) + with self.assertWarns(DeprecationWarning): + self.assertRaises(ValueError, math.factorial, -1.0) + with self.assertWarns(DeprecationWarning): + self.assertRaises(ValueError, math.factorial, -1e100) + self.assertRaises(TypeError, math.factorial, decimal.Decimal('5')) + self.assertRaises(TypeError, math.factorial, decimal.Decimal('5.2')) + self.assertRaises(TypeError, math.factorial, "5") + + # Other implementations may place different upper bounds. + @support.cpython_only + def testFactorialHugeInputs(self): + # Currently raises OverflowError for inputs that are too large + # to fit into a C long. + self.assertRaises(OverflowError, math.factorial, 10**100) + with self.assertWarns(DeprecationWarning): + self.assertRaises(OverflowError, math.factorial, 1e100) + + @unittest.skip('TODO RustPython') + def testFloor(self): + self.assertRaises(TypeError, math.floor) + self.assertEqual(int, type(math.floor(0.5))) + self.assertEqual(math.floor(0.5), 0) + self.assertEqual(math.floor(1.0), 1) + self.assertEqual(math.floor(1.5), 1) + self.assertEqual(math.floor(-0.5), -1) + self.assertEqual(math.floor(-1.0), -1) + self.assertEqual(math.floor(-1.5), -2) + #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 FloatFloor(float): + def __floor__(self): + return 42 + class TestNoFloor: + pass + self.assertEqual(math.floor(TestFloor()), 42) + self.assertEqual(math.floor(FloatFloor()), 42) + self.assertEqual(math.floor(FloatLike(41.9)), 41) + 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])) + + + # TODO Rustpython + # @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')), + # ([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')), + # ] + + # # Telescoping sum, with exact differences (due to Sterbenz) + # terms = [1.7**i for i in range(1001)] + # test_values.append(( + # [terms[i+1] - terms[i] for i in range(1000)] + [-terms[1000]], + # -terms[0] + # )) + + # 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)) + + + # Python 3.9 + 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) + + x = 434610456570399902378880679233098819019853229470286994367836600566 + y = 1064502245825115327754847244914921553977 + for c in (652560, + 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.assertEqual(gcd(), 0) + self.assertEqual(gcd(120), 120) + self.assertEqual(gcd(-120), 120) + self.assertEqual(gcd(120, 84, 102), 6) + self.assertEqual(gcd(120, 1, 84), 1) + + self.assertRaises(TypeError, gcd, 120.0) + self.assertRaises(TypeError, gcd, 120.0, 84) + self.assertRaises(TypeError, gcd, 120, 84.0) + self.assertRaises(TypeError, gcd, 120, 1, 84.0) + #self.assertEqual(gcd(MyIndexable(120), MyIndexable(84)), 12) # TODO RustPython + + @unittest.skip('TODO: RustPython float support') + def testHypot(self): + from decimal import Decimal + from fractions import Fraction + + hypot = math.hypot + + # Test different numbers of arguments (from zero to five) + # against a straightforward pure python implementation + args = math.e, math.pi, math.sqrt(2.0), math.gamma(3.5), math.sin(2.1) + for i in range(len(args)+1): + self.assertAlmostEqual( + hypot(*args[:i]), + math.sqrt(sum(s**2 for s in args[:i])) + ) + + # Test allowable types (those with __float__) + self.assertEqual(hypot(12.0, 5.0), 13.0) + self.assertEqual(hypot(12, 5), 13) + self.assertEqual(hypot(Decimal(12), Decimal(5)), 13) + self.assertEqual(hypot(Fraction(12, 32), Fraction(5, 32)), Fraction(13, 32)) + self.assertEqual(hypot(bool(1), bool(0), bool(1), bool(1)), math.sqrt(3)) + + # Test corner cases + self.assertEqual(hypot(0.0, 0.0), 0.0) # Max input is zero + self.assertEqual(hypot(-10.5), 10.5) # Negative input + self.assertEqual(hypot(), 0.0) # Negative input + self.assertEqual(1.0, + math.copysign(1.0, hypot(-0.0)) # Convert negative zero to positive zero + ) + self.assertEqual( # Handling of moving max to the end + hypot(1.5, 1.5, 0.5), + hypot(1.5, 0.5, 1.5), + ) + + # Test handling of bad arguments + with self.assertRaises(TypeError): # Reject keyword args + hypot(x=1) + with self.assertRaises(TypeError): # Reject values without __float__ + hypot(1.1, 'string', 2.2) + int_too_big_for_float = 10 ** (sys.float_info.max_10_exp + 5) + with self.assertRaises((ValueError, OverflowError)): + hypot(1, int_too_big_for_float) + + # Any infinity gives positive infinity. + self.assertEqual(hypot(INF), INF) + self.assertEqual(hypot(0, INF), INF) + self.assertEqual(hypot(10, INF), INF) + self.assertEqual(hypot(-10, INF), INF) + self.assertEqual(hypot(NAN, INF), INF) + self.assertEqual(hypot(INF, NAN), INF) + self.assertEqual(hypot(NINF, NAN), INF) + self.assertEqual(hypot(NAN, NINF), INF) + self.assertEqual(hypot(-INF, INF), INF) + self.assertEqual(hypot(-INF, -INF), INF) + self.assertEqual(hypot(10, -INF), INF) + + # If no infinity, any NaN gives a NaN. + self.assertTrue(math.isnan(hypot(NAN))) + self.assertTrue(math.isnan(hypot(0, NAN))) + self.assertTrue(math.isnan(hypot(NAN, 10))) + self.assertTrue(math.isnan(hypot(10, NAN))) + self.assertTrue(math.isnan(hypot(NAN, NAN))) + self.assertTrue(math.isnan(hypot(NAN))) + + # Verify scaling for extremely large values + fourthmax = FLOAT_MAX / 4.0 + for n in range(32): + self.assertEqual(hypot(*([fourthmax]*n)), fourthmax * math.sqrt(n)) + + # Verify scaling for extremely small values + for exp in range(32): + scale = FLOAT_MIN / 2.0 ** exp + self.assertEqual(math.hypot(4*scale, 3*scale), 5*scale) + + @unittest.skip('RustPython') + def testDist(self): + from decimal import Decimal as D + from fractions import Fraction as F + + dist = math.dist + sqrt = math.sqrt + + # Simple exact cases + self.assertEqual(dist((1.0, 2.0, 3.0), (4.0, 2.0, -1.0)), 5.0) + self.assertEqual(dist((1, 2, 3), (4, 2, -1)), 5.0) + + # Test different numbers of arguments (from zero to nine) + # against a straightforward pure python implementation + for i in range(9): + for j in range(5): + p = tuple(random.uniform(-5, 5) for k in range(i)) + q = tuple(random.uniform(-5, 5) for k in range(i)) + self.assertAlmostEqual( + dist(p, q), + sqrt(sum((px - qx) ** 2.0 for px, qx in zip(p, q))) + ) + + # Test non-tuple inputs + self.assertEqual(dist([1.0, 2.0, 3.0], [4.0, 2.0, -1.0]), 5.0) + self.assertEqual(dist(iter([1.0, 2.0, 3.0]), iter([4.0, 2.0, -1.0])), 5.0) + + # Test allowable types (those with __float__) + self.assertEqual(dist((14.0, 1.0), (2.0, -4.0)), 13.0) + self.assertEqual(dist((14, 1), (2, -4)), 13) + self.assertEqual(dist((D(14), D(1)), (D(2), D(-4))), D(13)) + self.assertEqual(dist((F(14, 32), F(1, 32)), (F(2, 32), F(-4, 32))), + F(13, 32)) + self.assertEqual(dist((True, True, False, True, False), + (True, False, True, True, False)), + sqrt(2.0)) + + # Test corner cases + self.assertEqual(dist((13.25, 12.5, -3.25), + (13.25, 12.5, -3.25)), + 0.0) # Distance with self is zero + self.assertEqual(dist((), ()), 0.0) # Zero-dimensional case + self.assertEqual(1.0, # Convert negative zero to positive zero + math.copysign(1.0, dist((-0.0,), (0.0,))) + ) + self.assertEqual(1.0, # Convert negative zero to positive zero + math.copysign(1.0, dist((0.0,), (-0.0,))) + ) + self.assertEqual( # Handling of moving max to the end + dist((1.5, 1.5, 0.5), (0, 0, 0)), + dist((1.5, 0.5, 1.5), (0, 0, 0)) + ) + + # Verify tuple subclasses are allowed + class T(tuple): + pass + self.assertEqual(dist(T((1, 2, 3)), ((4, 2, -1))), 5.0) + + # Test handling of bad arguments + with self.assertRaises(TypeError): # Reject keyword args + dist(p=(1, 2, 3), q=(4, 5, 6)) + with self.assertRaises(TypeError): # Too few args + dist((1, 2, 3)) + with self.assertRaises(TypeError): # Too many args + dist((1, 2, 3), (4, 5, 6), (7, 8, 9)) + with self.assertRaises(TypeError): # Scalars not allowed + dist(1, 2) + with self.assertRaises(TypeError): # Reject values without __float__ + dist((1.1, 'string', 2.2), (1, 2, 3)) + with self.assertRaises(ValueError): # Check dimension agree + dist((1, 2, 3, 4), (5, 6, 7)) + with self.assertRaises(ValueError): # Check dimension agree + dist((1, 2, 3), (4, 5, 6, 7)) + with self.assertRaises(TypeError): # Rejects invalid types + dist("abc", "xyz") + int_too_big_for_float = 10 ** (sys.float_info.max_10_exp + 5) + with self.assertRaises((ValueError, OverflowError)): + dist((1, int_too_big_for_float), (2, 3)) + with self.assertRaises((ValueError, OverflowError)): + dist((2, 3), (1, int_too_big_for_float)) + + # Verify that the one dimensional case is equivalent to abs() + for i in range(20): + p, q = random.random(), random.random() + self.assertEqual(dist((p,), (q,)), abs(p - q)) + + # Test special values + values = [NINF, -10.5, -0.0, 0.0, 10.5, INF, NAN] + for p in itertools.product(values, repeat=3): + for q in itertools.product(values, repeat=3): + diffs = [px - qx for px, qx in zip(p, q)] + if any(map(math.isinf, diffs)): + # Any infinite difference gives positive infinity. + self.assertEqual(dist(p, q), INF) + elif any(map(math.isnan, diffs)): + # If no infinity, any NaN gives a NaN. + self.assertTrue(math.isnan(dist(p, q))) + + # Verify scaling for extremely large values + fourthmax = FLOAT_MAX / 4.0 + for n in range(32): + p = (fourthmax,) * n + q = (0.0,) * n + self.assertEqual(dist(p, q), fourthmax * math.sqrt(n)) + self.assertEqual(dist(q, p), fourthmax * math.sqrt(n)) + + # Verify scaling for extremely small values + for exp in range(32): + scale = FLOAT_MIN / 2.0 ** exp + p = (4*scale, 3*scale) + q = (0.0, 0.0) + self.assertEqual(math.dist(p, q), 5*scale) + self.assertEqual(math.dist(q, p), 5*scale) + + @unittest.skip('TODO RustPython') + def testIsqrt(self): + # Test a variety of inputs, large and small. + test_values = ( + list(range(1000)) + + list(range(10**6 - 1000, 10**6 + 1000)) + + [2**e + i for e in range(60, 200) for i in range(-40, 40)] + + [3**9999, 10**5001] + ) + + for value in test_values: + with self.subTest(value=value): + s = math.isqrt(value) + self.assertIs(type(s), int) + self.assertLessEqual(s*s, value) + self.assertLess(value, (s+1)*(s+1)) + + # Negative values + with self.assertRaises(ValueError): + math.isqrt(-1) + + # Integer-like things + s = math.isqrt(True) + self.assertIs(type(s), int) + self.assertEqual(s, 1) + + s = math.isqrt(False) + self.assertIs(type(s), int) + self.assertEqual(s, 0) + + class IntegerLike(object): + def __init__(self, value): + self.value = value + + def __index__(self): + return self.value + + s = math.isqrt(IntegerLike(1729)) + self.assertIs(type(s), int) + self.assertEqual(s, 41) + + with self.assertRaises(ValueError): + math.isqrt(IntegerLike(-3)) + + # Non-integer-like things + bad_values = [ + 3.5, "a string", decimal.Decimal("3.5"), 3.5j, + 100.0, -4.0, + ] + for value in bad_values: + with self.subTest(value=value): + with self.assertRaises(TypeError): + math.isqrt(value) + + # Python 3.9 + def testlcm(self): + lcm = math.lcm + self.assertEqual(lcm(0, 0), 0) + self.assertEqual(lcm(1, 0), 0) + self.assertEqual(lcm(-1, 0), 0) + self.assertEqual(lcm(0, 1), 0) + self.assertEqual(lcm(0, -1), 0) + self.assertEqual(lcm(7, 1), 7) + self.assertEqual(lcm(7, -1), 7) + self.assertEqual(lcm(-23, 15), 345) + self.assertEqual(lcm(120, 84), 840) + self.assertEqual(lcm(84, -120), 840) + self.assertEqual(lcm(1216342683557601535506311712, + 436522681849110124616458784), + 16592536571065866494401400422922201534178938447014944) + + x = 43461045657039990237 + y = 10645022458251153277 + for c in (652560, + 57655923087165495981): + a = x * c + b = y * c + d = x * y * c + self.assertEqual(lcm(a, b), d) + self.assertEqual(lcm(b, a), d) + self.assertEqual(lcm(-a, b), d) + self.assertEqual(lcm(b, -a), d) + self.assertEqual(lcm(a, -b), d) + self.assertEqual(lcm(-b, a), d) + self.assertEqual(lcm(-a, -b), d) + self.assertEqual(lcm(-b, -a), d) + + self.assertEqual(lcm(), 1) + self.assertEqual(lcm(120), 120) + self.assertEqual(lcm(-120), 120) + self.assertEqual(lcm(120, 84, 102), 14280) + self.assertEqual(lcm(120, 0, 84), 0) + + self.assertRaises(TypeError, lcm, 120.0) + self.assertRaises(TypeError, lcm, 120.0, 84) + self.assertRaises(TypeError, lcm, 120, 84.0) + self.assertRaises(TypeError, lcm, 120, 0, 84.0) + # self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 840) # TODO RustPython + + @unittest.skip('TODO RustPython') + 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))) + + @unittest.skip('TODO RustPython') + 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))) + + @unittest.skip('TODO RustPython') + 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) + + # TODO Rustpython + # @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))) + + # TODO Rustpython + # @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])) + + @unittest.skip('TODO RustPython') + 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) + + # TODO Rustpython + # @requires_IEEE_754 + # def testRemainder(self): + # from fractions import Fraction + + # def validate_spec(x, y, r): + # """ + # Check that r matches remainder(x, y) according to the IEEE 754 + # specification. Assumes that x, y and r are finite and y is nonzero. + # """ + # fx, fy, fr = Fraction(x), Fraction(y), Fraction(r) + # # r should not exceed y/2 in absolute value + # self.assertLessEqual(abs(fr), abs(fy/2)) + # # x - r should be an exact integer multiple of y + # n = (fx - fr) / fy + # self.assertEqual(n, int(n)) + # if abs(fr) == abs(fy/2): + # # If |r| == |y/2|, n should be even. + # self.assertEqual(n/2, int(n/2)) + + # # triples (x, y, remainder(x, y)) in hexadecimal form. + # testcases = [ + # # Remainders modulo 1, showing the ties-to-even behaviour. + # '-4.0 1 -0.0', + # '-3.8 1 0.8', + # '-3.0 1 -0.0', + # '-2.8 1 -0.8', + # '-2.0 1 -0.0', + # '-1.8 1 0.8', + # '-1.0 1 -0.0', + # '-0.8 1 -0.8', + # '-0.0 1 -0.0', + # ' 0.0 1 0.0', + # ' 0.8 1 0.8', + # ' 1.0 1 0.0', + # ' 1.8 1 -0.8', + # ' 2.0 1 0.0', + # ' 2.8 1 0.8', + # ' 3.0 1 0.0', + # ' 3.8 1 -0.8', + # ' 4.0 1 0.0', + + # # Reductions modulo 2*pi + # '0x0.0p+0 0x1.921fb54442d18p+2 0x0.0p+0', + # '0x1.921fb54442d18p+0 0x1.921fb54442d18p+2 0x1.921fb54442d18p+0', + # '0x1.921fb54442d17p+1 0x1.921fb54442d18p+2 0x1.921fb54442d17p+1', + # '0x1.921fb54442d18p+1 0x1.921fb54442d18p+2 0x1.921fb54442d18p+1', + # '0x1.921fb54442d19p+1 0x1.921fb54442d18p+2 -0x1.921fb54442d17p+1', + # '0x1.921fb54442d17p+2 0x1.921fb54442d18p+2 -0x0.0000000000001p+2', + # '0x1.921fb54442d18p+2 0x1.921fb54442d18p+2 0x0p0', + # '0x1.921fb54442d19p+2 0x1.921fb54442d18p+2 0x0.0000000000001p+2', + # '0x1.2d97c7f3321d1p+3 0x1.921fb54442d18p+2 0x1.921fb54442d14p+1', + # '0x1.2d97c7f3321d2p+3 0x1.921fb54442d18p+2 -0x1.921fb54442d18p+1', + # '0x1.2d97c7f3321d3p+3 0x1.921fb54442d18p+2 -0x1.921fb54442d14p+1', + # '0x1.921fb54442d17p+3 0x1.921fb54442d18p+2 -0x0.0000000000001p+3', + # '0x1.921fb54442d18p+3 0x1.921fb54442d18p+2 0x0p0', + # '0x1.921fb54442d19p+3 0x1.921fb54442d18p+2 0x0.0000000000001p+3', + # '0x1.f6a7a2955385dp+3 0x1.921fb54442d18p+2 0x1.921fb54442d14p+1', + # '0x1.f6a7a2955385ep+3 0x1.921fb54442d18p+2 0x1.921fb54442d18p+1', + # '0x1.f6a7a2955385fp+3 0x1.921fb54442d18p+2 -0x1.921fb54442d14p+1', + # '0x1.1475cc9eedf00p+5 0x1.921fb54442d18p+2 0x1.921fb54442d10p+1', + # '0x1.1475cc9eedf01p+5 0x1.921fb54442d18p+2 -0x1.921fb54442d10p+1', + + # # Symmetry with respect to signs. + # ' 1 0.c 0.4', + # '-1 0.c -0.4', + # ' 1 -0.c 0.4', + # '-1 -0.c -0.4', + # ' 1.4 0.c -0.4', + # '-1.4 0.c 0.4', + # ' 1.4 -0.c -0.4', + # '-1.4 -0.c 0.4', + + # # Huge modulus, to check that the underlying algorithm doesn't + # # rely on 2.0 * modulus being representable. + # '0x1.dp+1023 0x1.4p+1023 0x0.9p+1023', + # '0x1.ep+1023 0x1.4p+1023 -0x0.ap+1023', + # '0x1.fp+1023 0x1.4p+1023 -0x0.9p+1023', + # ] + + # for case in testcases: + # with self.subTest(case=case): + # x_hex, y_hex, expected_hex = case.split() + # x = float.fromhex(x_hex) + # y = float.fromhex(y_hex) + # expected = float.fromhex(expected_hex) + # validate_spec(x, y, expected) + # actual = math.remainder(x, y) + # # Cheap way of checking that the floats are + # # as identical as we need them to be. + # self.assertEqual(actual.hex(), expected.hex()) + + # # Test tiny subnormal modulus: there's potential for + # # getting the implementation wrong here (for example, + # # by assuming that modulus/2 is exactly representable). + # tiny = float.fromhex('1p-1074') # min +ve subnormal + # for n in range(-25, 25): + # if n == 0: + # continue + # y = n * tiny + # for m in range(100): + # x = m * tiny + # actual = math.remainder(x, y) + # validate_spec(x, y, actual) + # actual = math.remainder(-x, y) + # validate_spec(-x, y, actual) + + # # Special values. + # # NaNs should propagate as usual. + # for value in [NAN, 0.0, -0.0, 2.0, -2.3, NINF, INF]: + # self.assertIsNaN(math.remainder(NAN, value)) + # self.assertIsNaN(math.remainder(value, NAN)) + + # # remainder(x, inf) is x, for non-nan non-infinite x. + # for value in [-2.3, -0.0, 0.0, 2.3]: + # self.assertEqual(math.remainder(value, INF), value) + # self.assertEqual(math.remainder(value, NINF), value) + + # # remainder(x, 0) and remainder(infinity, x) for non-NaN x are invalid + # # operations according to IEEE 754-2008 7.2(f), and should raise. + # for value in [NINF, -2.3, -0.0, 0.0, 2.3, INF]: + # with self.assertRaises(ValueError): + # math.remainder(INF, value) + # with self.assertRaises(ValueError): + # math.remainder(NINF, value) + # with self.assertRaises(ValueError): + # math.remainder(value, 0.0) + # with self.assertRaises(ValueError): + # math.remainder(value, -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))) + + @unittest.skip('TODO RustPython') + 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))) + + @unittest.skip('TODO RustPython') + 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=math.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))) + + # TODO Rustpython + # @requires_IEEE_754 + # 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: + def __trunc__(self): + return 23 + class FloatTrunc(float): + def __trunc__(self): + return 23 + class TestNoTrunc: + pass + + self.assertEqual(math.trunc(TestTrunc()), 23) + self.assertEqual(math.trunc(FloatTrunc()), 23) + + self.assertRaises(TypeError, math.trunc) + self.assertRaises(TypeError, math.trunc, 1, 2) + self.assertRaises(TypeError, math.trunc, FloatLike(23.5)) + 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.)) + + # TODO Rustpython + # @requires_IEEE_754 + # def test_nan_constant(self): + # self.assertTrue(math.isnan(math.nan)) + + # TODO Rustpython + # @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.skip('TODO RustPython') + @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") + + # TODO Rustpython + # @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)) + + # TODO Rustpython + # @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)) + + @unittest.skip('TODO RustPython') + def test_prod(self): + prod = math.prod + self.assertEqual(prod([]), 1) + self.assertEqual(prod([], start=5), 5) + self.assertEqual(prod(list(range(2,8))), 5040) + self.assertEqual(prod(iter(list(range(2,8)))), 5040) + self.assertEqual(prod(range(1, 10), start=10), 3628800) + + self.assertEqual(prod([1, 2, 3, 4, 5]), 120) + self.assertEqual(prod([1.0, 2.0, 3.0, 4.0, 5.0]), 120.0) + self.assertEqual(prod([1, 2, 3, 4.0, 5.0]), 120.0) + self.assertEqual(prod([1.0, 2.0, 3.0, 4, 5]), 120.0) + + # Test overflow in fast-path for integers + self.assertEqual(prod([1, 1, 2**32, 1, 1]), 2**32) + # Test overflow in fast-path for floats + self.assertEqual(prod([1.0, 1.0, 2**32, 1, 1]), float(2**32)) + + self.assertRaises(TypeError, prod) + self.assertRaises(TypeError, prod, 42) + self.assertRaises(TypeError, prod, ['a', 'b', 'c']) + self.assertRaises(TypeError, prod, ['a', 'b', 'c'], '') + self.assertRaises(TypeError, prod, [b'a', b'c'], b'') + values = [bytearray(b'a'), bytearray(b'b')] + self.assertRaises(TypeError, prod, values, bytearray(b'')) + self.assertRaises(TypeError, prod, [[1], [2], [3]]) + self.assertRaises(TypeError, prod, [{2:3}]) + self.assertRaises(TypeError, prod, [{2:3}]*2, {2:3}) + self.assertRaises(TypeError, prod, [[1], [2], [3]], []) + with self.assertRaises(TypeError): + prod([10, 20], [30, 40]) # start is a keyword-only argument + + self.assertEqual(prod([0, 1, 2, 3]), 0) + self.assertEqual(prod([1, 0, 2, 3]), 0) + self.assertEqual(prod([1, 2, 3, 0]), 0) + + def _naive_prod(iterable, start=1): + for elem in iterable: + start *= elem + return start + + # Big integers + + iterable = range(1, 10000) + self.assertEqual(prod(iterable), _naive_prod(iterable)) + iterable = range(-10000, -1) + self.assertEqual(prod(iterable), _naive_prod(iterable)) + iterable = range(-1000, 1000) + self.assertEqual(prod(iterable), 0) + + # Big floats + + iterable = [float(x) for x in range(1, 1000)] + self.assertEqual(prod(iterable), _naive_prod(iterable)) + iterable = [float(x) for x in range(-1000, -1)] + self.assertEqual(prod(iterable), _naive_prod(iterable)) + iterable = [float(x) for x in range(-1000, 1000)] + self.assertIsNaN(prod(iterable)) + + # Float tests + + self.assertIsNaN(prod([1, 2, 3, float("nan"), 2, 3])) + self.assertIsNaN(prod([1, 0, float("nan"), 2, 3])) + self.assertIsNaN(prod([1, float("nan"), 0, 3])) + self.assertIsNaN(prod([1, float("inf"), float("nan"),3])) + self.assertIsNaN(prod([1, float("-inf"), float("nan"),3])) + self.assertIsNaN(prod([1, float("nan"), float("inf"),3])) + self.assertIsNaN(prod([1, float("nan"), float("-inf"),3])) + + self.assertEqual(prod([1, 2, 3, float('inf'),-3,4]), float('-inf')) + self.assertEqual(prod([1, 2, 3, float('-inf'),-3,4]), float('inf')) + + self.assertIsNaN(prod([1,2,0,float('inf'), -3, 4])) + self.assertIsNaN(prod([1,2,0,float('-inf'), -3, 4])) + self.assertIsNaN(prod([1, 2, 3, float('inf'), -3, 0, 3])) + self.assertIsNaN(prod([1, 2, 3, float('-inf'), -3, 0, 2])) + + # Type preservation + + self.assertEqual(type(prod([1, 2, 3, 4, 5, 6])), int) + self.assertEqual(type(prod([1, 2.0, 3, 4, 5, 6])), float) + self.assertEqual(type(prod(range(1, 10000))), int) + self.assertEqual(type(prod(range(1, 10000), start=1.0)), float) + self.assertEqual(type(prod([1, decimal.Decimal(2.0), 3, 4, 5, 6])), + decimal.Decimal) + + @unittest.skip('TODO RustPython') + def testPerm(self): + perm = math.perm + factorial = math.factorial + # Test if factorial definition is satisfied + for n in range(100): + for k in range(n + 1): + self.assertEqual(perm(n, k), + factorial(n) // factorial(n - k)) + + # Test for Pascal's identity + for n in range(1, 100): + for k in range(1, n): + self.assertEqual(perm(n, k), perm(n - 1, k - 1) * k + perm(n - 1, k)) + + # Test corner cases + for n in range(1, 100): + self.assertEqual(perm(n, 0), 1) + self.assertEqual(perm(n, 1), n) + self.assertEqual(perm(n, n), factorial(n)) + + # Test one argument form + for n in range(20): + self.assertEqual(perm(n), factorial(n)) + self.assertEqual(perm(n, None), factorial(n)) + + # Raises TypeError if any argument is non-integer or argument count is + # not 1 or 2 + self.assertRaises(TypeError, perm, 10, 1.0) + self.assertRaises(TypeError, perm, 10, decimal.Decimal(1.0)) + self.assertRaises(TypeError, perm, 10, "1") + self.assertRaises(TypeError, perm, 10.0, 1) + self.assertRaises(TypeError, perm, decimal.Decimal(10.0), 1) + self.assertRaises(TypeError, perm, "10", 1) + + self.assertRaises(TypeError, perm) + self.assertRaises(TypeError, perm, 10, 1, 3) + self.assertRaises(TypeError, perm) + + # Raises Value error if not k or n are negative numbers + self.assertRaises(ValueError, perm, -1, 1) + self.assertRaises(ValueError, perm, -2**1000, 1) + self.assertRaises(ValueError, perm, 1, -1) + self.assertRaises(ValueError, perm, 1, -2**1000) + + # Returns zero if k is greater than n + self.assertEqual(perm(1, 2), 0) + self.assertEqual(perm(1, 2**1000), 0) + + n = 2**1000 + self.assertEqual(perm(n, 0), 1) + self.assertEqual(perm(n, 1), n) + self.assertEqual(perm(n, 2), n * (n-1)) + if support.check_impl_detail(cpython=True): + self.assertRaises(OverflowError, perm, n, n) + + for n, k in (True, True), (True, False), (False, False): + self.assertEqual(perm(n, k), 1) + self.assertIs(type(perm(n, k)), int) + self.assertEqual(perm(IntSubclass(5), IntSubclass(2)), 20) + self.assertEqual(perm(MyIndexable(5), MyIndexable(2)), 20) + for k in range(3): + self.assertIs(type(perm(IntSubclass(5), IntSubclass(k))), int) + self.assertIs(type(perm(MyIndexable(5), MyIndexable(k))), int) + + @unittest.skip('TODO RustPython') + def testComb(self): + comb = math.comb + factorial = math.factorial + # Test if factorial definition is satisfied + for n in range(100): + for k in range(n + 1): + self.assertEqual(comb(n, k), factorial(n) + // (factorial(k) * factorial(n - k))) + + # Test for Pascal's identity + for n in range(1, 100): + for k in range(1, n): + self.assertEqual(comb(n, k), comb(n - 1, k - 1) + comb(n - 1, k)) + + # Test corner cases + for n in range(100): + self.assertEqual(comb(n, 0), 1) + self.assertEqual(comb(n, n), 1) + + for n in range(1, 100): + self.assertEqual(comb(n, 1), n) + self.assertEqual(comb(n, n - 1), n) + + # Test Symmetry + for n in range(100): + for k in range(n // 2): + self.assertEqual(comb(n, k), comb(n, n - k)) + + # Raises TypeError if any argument is non-integer or argument count is + # not 2 + self.assertRaises(TypeError, comb, 10, 1.0) + self.assertRaises(TypeError, comb, 10, decimal.Decimal(1.0)) + self.assertRaises(TypeError, comb, 10, "1") + self.assertRaises(TypeError, comb, 10.0, 1) + self.assertRaises(TypeError, comb, decimal.Decimal(10.0), 1) + self.assertRaises(TypeError, comb, "10", 1) + + self.assertRaises(TypeError, comb, 10) + self.assertRaises(TypeError, comb, 10, 1, 3) + self.assertRaises(TypeError, comb) + + # Raises Value error if not k or n are negative numbers + self.assertRaises(ValueError, comb, -1, 1) + self.assertRaises(ValueError, comb, -2**1000, 1) + self.assertRaises(ValueError, comb, 1, -1) + self.assertRaises(ValueError, comb, 1, -2**1000) + + # Returns zero if k is greater than n + self.assertEqual(comb(1, 2), 0) + self.assertEqual(comb(1, 2**1000), 0) + + n = 2**1000 + self.assertEqual(comb(n, 0), 1) + self.assertEqual(comb(n, 1), n) + self.assertEqual(comb(n, 2), n * (n-1) // 2) + self.assertEqual(comb(n, n), 1) + self.assertEqual(comb(n, n-1), n) + self.assertEqual(comb(n, n-2), n * (n-1) // 2) + if support.check_impl_detail(cpython=True): + self.assertRaises(OverflowError, comb, n, n//2) + + for n, k in (True, True), (True, False), (False, False): + self.assertEqual(comb(n, k), 1) + self.assertIs(type(comb(n, k)), int) + self.assertEqual(comb(IntSubclass(5), IntSubclass(2)), 10) + self.assertEqual(comb(MyIndexable(5), MyIndexable(2)), 10) + for k in range(3): + self.assertIs(type(comb(IntSubclass(5), IntSubclass(k))), int) + self.assertIs(type(comb(MyIndexable(5), MyIndexable(k))), int) + + # TODO Rustpython + # @requires_IEEE_754 + # def test_nextafter(self): + # # around 2^52 and 2^63 + # self.assertEqual(math.nextafter(4503599627370496.0, -INF), + # 4503599627370495.5) + # self.assertEqual(math.nextafter(4503599627370496.0, INF), + # 4503599627370497.0) + # self.assertEqual(math.nextafter(9223372036854775808.0, 0.0), + # 9223372036854774784.0) + # self.assertEqual(math.nextafter(-9223372036854775808.0, 0.0), + # -9223372036854774784.0) + + # # around 1.0 + # self.assertEqual(math.nextafter(1.0, -INF), + # float.fromhex('0x1.fffffffffffffp-1')) + # self.assertEqual(math.nextafter(1.0, INF), + # float.fromhex('0x1.0000000000001p+0')) + + # # x == y: y is returned + # self.assertEqual(math.nextafter(2.0, 2.0), 2.0) + # self.assertEqualSign(math.nextafter(-0.0, +0.0), +0.0) + # self.assertEqualSign(math.nextafter(+0.0, -0.0), -0.0) + + # # around 0.0 + # smallest_subnormal = sys.float_info.min * sys.float_info.epsilon + # self.assertEqual(math.nextafter(+0.0, INF), smallest_subnormal) + # self.assertEqual(math.nextafter(-0.0, INF), smallest_subnormal) + # self.assertEqual(math.nextafter(+0.0, -INF), -smallest_subnormal) + # self.assertEqual(math.nextafter(-0.0, -INF), -smallest_subnormal) + # self.assertEqualSign(math.nextafter(smallest_subnormal, +0.0), +0.0) + # self.assertEqualSign(math.nextafter(-smallest_subnormal, +0.0), -0.0) + # self.assertEqualSign(math.nextafter(smallest_subnormal, -0.0), +0.0) + # self.assertEqualSign(math.nextafter(-smallest_subnormal, -0.0), -0.0) + + # # around infinity + # largest_normal = sys.float_info.max + # self.assertEqual(math.nextafter(INF, 0.0), largest_normal) + # self.assertEqual(math.nextafter(-INF, 0.0), -largest_normal) + # self.assertEqual(math.nextafter(largest_normal, INF), INF) + # self.assertEqual(math.nextafter(-largest_normal, -INF), -INF) + + # # NaN + # self.assertIsNaN(math.nextafter(NAN, 1.0)) + # self.assertIsNaN(math.nextafter(1.0, NAN)) + # self.assertIsNaN(math.nextafter(NAN, NAN)) + + # @requires_IEEE_754 + # def test_ulp(self): + # self.assertEqual(math.ulp(1.0), sys.float_info.epsilon) + # # use int ** int rather than float ** int to not rely on pow() accuracy + # self.assertEqual(math.ulp(2 ** 52), 1.0) + # self.assertEqual(math.ulp(2 ** 53), 2.0) + # self.assertEqual(math.ulp(2 ** 64), 4096.0) + + # # min and max + # self.assertEqual(math.ulp(0.0), + # sys.float_info.min * sys.float_info.epsilon) + # self.assertEqual(math.ulp(FLOAT_MAX), + # FLOAT_MAX - math.nextafter(FLOAT_MAX, -INF)) + + # # special cases + # self.assertEqual(math.ulp(INF), INF) + # self.assertIsNaN(math.ulp(math.nan)) + + # # negative number: ulp(-x) == ulp(x) + # for x in (0.0, 1.0, 2 ** 52, 2 ** 64, INF): + # with self.subTest(x=x): + # self.assertEqual(math.ulp(-x), math.ulp(x)) + + @unittest.skip('TODO RustPython') + def test_issue39871(self): + # A SystemError should not be raised if the first arg to atan2(), + # copysign(), or remainder() cannot be converted to a float. + class F: + def __float__(self): + self.converted = True + 1/0 + for func in math.atan2, math.copysign, math.remainder: + y = F() + with self.assertRaises(TypeError): + func("not a number", y) + + # There should not have been any attempt to convert the second + # argument to a float. + self.assertFalse(getattr(y, "converted", False)) + + # Custom assertions. + + def assertIsNaN(self, value): + if not math.isnan(value): + self.fail("Expected a NaN, got {!r}.".format(value)) + + def assertEqualSign(self, x, y): + """Similar to assertEqual(), but compare also the sign with copysign(). + Function useful to compare signed zeros. + """ + self.assertEqual(x, y) + self.assertEqual(math.copysign(1.0, x), math.copysign(1.0, y)) + + +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) + + @unittest.skip('TODO RustPython') + 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) + + @unittest.skip('TODO Rustpython') + 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() \ No newline at end of file diff --git a/vm/src/stdlib/math.rs b/vm/src/stdlib/math.rs index 6873e4352e..cb2c812cab 100644 --- a/vm/src/stdlib/math.rs +++ b/vm/src/stdlib/math.rs @@ -9,9 +9,9 @@ use statrs::function::gamma::{gamma, ln_gamma}; use num_bigint::BigInt; use num_traits::{One, Zero}; -use crate::function::OptionalArg; +use crate::function::{Args, OptionalArg}; use crate::obj::objfloat::{self, IntoPyFloat, PyFloatRef}; -use crate::obj::objint::{self, PyIntRef}; +use crate::obj::objint::{self, PyInt, PyIntRef}; use crate::obj::objtype; use crate::pyobject::{Either, PyObjectRef, PyResult, TypeProtocol}; use crate::vm::VirtualMachine; @@ -272,9 +272,33 @@ fn math_ldexp( Ok(value * (2_f64).powf(objint::try_float(i.as_bigint(), vm)?)) } -fn math_gcd(a: PyIntRef, b: PyIntRef) -> BigInt { +fn math_perf_arb_len_int_op(args: Args, op: F, default: BigInt) -> BigInt +where + F: Fn(&BigInt, &PyInt) -> BigInt, +{ + let argvec = args.into_vec(); + + if argvec.is_empty() { + return default; + } else if argvec.len() == 1 { + return op(argvec[0].as_bigint(), &argvec[0]); + } + + let mut res = argvec[0].as_bigint().clone(); + for num in argvec[1..].iter() { + res = op(&res, &num) + } + res +} + +fn math_gcd(args: Args) -> BigInt { + use num_integer::Integer; + math_perf_arb_len_int_op(args, |x, y| x.gcd(y.as_bigint()), BigInt::zero()) +} + +fn math_lcm(args: Args) -> BigInt { use num_integer::Integer; - a.as_bigint().gcd(b.as_bigint()) + math_perf_arb_len_int_op(args, |x, y| x.lcm(y.as_bigint()), BigInt::one()) } fn math_factorial(value: PyIntRef, vm: &VirtualMachine) -> PyResult { @@ -436,6 +460,7 @@ pub fn make_module(vm: &VirtualMachine) -> PyObjectRef { // Gcd function "gcd" => ctx.new_function(math_gcd), + "lcm" => ctx.new_function(math_lcm), // Factorial function "factorial" => ctx.new_function(math_factorial),