| import fractions |
| import operator |
| import os |
| import random |
| import sys |
| import struct |
| import time |
| import unittest |
| |
| from test import support |
| from test.test_grammar import (VALID_UNDERSCORE_LITERALS, |
| INVALID_UNDERSCORE_LITERALS) |
| from math import isinf, isnan, copysign, ldexp |
| |
| INF = float("inf") |
| NAN = float("nan") |
| |
| have_getformat = hasattr(float, "__getformat__") |
| requires_getformat = unittest.skipUnless(have_getformat, |
| "requires __getformat__") |
| requires_setformat = unittest.skipUnless(hasattr(float, "__setformat__"), |
| "requires __setformat__") |
| |
| #locate file with float format test values |
| test_dir = os.path.dirname(__file__) or os.curdir |
| format_testfile = os.path.join(test_dir, 'formatfloat_testcases.txt') |
| |
| class FloatSubclass(float): |
| pass |
| |
| class OtherFloatSubclass(float): |
| pass |
| |
| class GeneralFloatCases(unittest.TestCase): |
| |
| def test_float(self): |
| self.assertEqual(float(3.14), 3.14) |
| self.assertEqual(float(314), 314.0) |
| self.assertEqual(float(" 3.14 "), 3.14) |
| self.assertRaises(ValueError, float, " 0x3.1 ") |
| self.assertRaises(ValueError, float, " -0x3.p-1 ") |
| self.assertRaises(ValueError, float, " +0x3.p-1 ") |
| self.assertRaises(ValueError, float, "++3.14") |
| self.assertRaises(ValueError, float, "+-3.14") |
| self.assertRaises(ValueError, float, "-+3.14") |
| self.assertRaises(ValueError, float, "--3.14") |
| self.assertRaises(ValueError, float, ".nan") |
| self.assertRaises(ValueError, float, "+.inf") |
| self.assertRaises(ValueError, float, ".") |
| self.assertRaises(ValueError, float, "-.") |
| self.assertRaises(TypeError, float, {}) |
| self.assertRaisesRegex(TypeError, "not 'dict'", float, {}) |
| # Lone surrogate |
| self.assertRaises(ValueError, float, '\uD8F0') |
| # check that we don't accept alternate exponent markers |
| self.assertRaises(ValueError, float, "-1.7d29") |
| self.assertRaises(ValueError, float, "3D-14") |
| self.assertEqual(float(" \u0663.\u0661\u0664 "), 3.14) |
| self.assertEqual(float("\N{EM SPACE}3.14\N{EN SPACE}"), 3.14) |
| # extra long strings should not be a problem |
| float(b'.' + b'1'*1000) |
| float('.' + '1'*1000) |
| # Invalid unicode string |
| # See bpo-34087 |
| self.assertRaises(ValueError, float, '\u3053\u3093\u306b\u3061\u306f') |
| |
| def test_underscores(self): |
| for lit in VALID_UNDERSCORE_LITERALS: |
| if not any(ch in lit for ch in 'jJxXoObB'): |
| self.assertEqual(float(lit), eval(lit)) |
| self.assertEqual(float(lit), float(lit.replace('_', ''))) |
| for lit in INVALID_UNDERSCORE_LITERALS: |
| if lit in ('0_7', '09_99'): # octals are not recognized here |
| continue |
| if not any(ch in lit for ch in 'jJxXoObB'): |
| self.assertRaises(ValueError, float, lit) |
| # Additional test cases; nan and inf are never valid as literals, |
| # only in the float() constructor, but we don't allow underscores |
| # in or around them. |
| self.assertRaises(ValueError, float, '_NaN') |
| self.assertRaises(ValueError, float, 'Na_N') |
| self.assertRaises(ValueError, float, 'IN_F') |
| self.assertRaises(ValueError, float, '-_INF') |
| self.assertRaises(ValueError, float, '-INF_') |
| # Check that we handle bytes values correctly. |
| self.assertRaises(ValueError, float, b'0_.\xff9') |
| |
| def test_non_numeric_input_types(self): |
| # Test possible non-numeric types for the argument x, including |
| # subclasses of the explicitly documented accepted types. |
| class CustomStr(str): pass |
| class CustomBytes(bytes): pass |
| class CustomByteArray(bytearray): pass |
| |
| factories = [ |
| bytes, |
| bytearray, |
| lambda b: CustomStr(b.decode()), |
| CustomBytes, |
| CustomByteArray, |
| memoryview, |
| ] |
| try: |
| from array import array |
| except ImportError: |
| pass |
| else: |
| factories.append(lambda b: array('B', b)) |
| |
| for f in factories: |
| x = f(b" 3.14 ") |
| with self.subTest(type(x)): |
| self.assertEqual(float(x), 3.14) |
| with self.assertRaisesRegex(ValueError, "could not convert"): |
| float(f(b'A' * 0x10)) |
| |
| def test_float_memoryview(self): |
| self.assertEqual(float(memoryview(b'12.3')[1:4]), 2.3) |
| self.assertEqual(float(memoryview(b'12.3\x00')[1:4]), 2.3) |
| self.assertEqual(float(memoryview(b'12.3 ')[1:4]), 2.3) |
| self.assertEqual(float(memoryview(b'12.3A')[1:4]), 2.3) |
| self.assertEqual(float(memoryview(b'12.34')[1:4]), 2.3) |
| |
| def test_error_message(self): |
| def check(s): |
| with self.assertRaises(ValueError, msg='float(%r)' % (s,)) as cm: |
| float(s) |
| self.assertEqual(str(cm.exception), |
| 'could not convert string to float: %r' % (s,)) |
| |
| check('\xbd') |
| check('123\xbd') |
| check(' 123 456 ') |
| check(b' 123 456 ') |
| |
| # non-ascii digits (error came from non-digit '!') |
| check('\u0663\u0661\u0664!') |
| # embedded NUL |
| check('123\x00') |
| check('123\x00 245') |
| check('123\x00245') |
| # byte string with embedded NUL |
| check(b'123\x00') |
| # non-UTF-8 byte string |
| check(b'123\xa0') |
| |
| @support.run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE') |
| def test_float_with_comma(self): |
| # set locale to something that doesn't use '.' for the decimal point |
| # float must not accept the locale specific decimal point but |
| # it still has to accept the normal python syntax |
| import locale |
| if not locale.localeconv()['decimal_point'] == ',': |
| self.skipTest('decimal_point is not ","') |
| |
| self.assertEqual(float(" 3.14 "), 3.14) |
| self.assertEqual(float("+3.14 "), 3.14) |
| self.assertEqual(float("-3.14 "), -3.14) |
| self.assertEqual(float(".14 "), .14) |
| self.assertEqual(float("3. "), 3.0) |
| self.assertEqual(float("3.e3 "), 3000.0) |
| self.assertEqual(float("3.2e3 "), 3200.0) |
| self.assertEqual(float("2.5e-1 "), 0.25) |
| self.assertEqual(float("5e-1"), 0.5) |
| self.assertRaises(ValueError, float, " 3,14 ") |
| self.assertRaises(ValueError, float, " +3,14 ") |
| self.assertRaises(ValueError, float, " -3,14 ") |
| self.assertRaises(ValueError, float, " 0x3.1 ") |
| self.assertRaises(ValueError, float, " -0x3.p-1 ") |
| self.assertRaises(ValueError, float, " +0x3.p-1 ") |
| self.assertEqual(float(" 25.e-1 "), 2.5) |
| self.assertAlmostEqual(float(" .25e-1 "), .025) |
| |
| def test_floatconversion(self): |
| # Make sure that calls to __float__() work properly |
| class Foo1(object): |
| def __float__(self): |
| return 42. |
| |
| class Foo2(float): |
| def __float__(self): |
| return 42. |
| |
| class Foo3(float): |
| def __new__(cls, value=0.): |
| return float.__new__(cls, 2*value) |
| |
| def __float__(self): |
| return self |
| |
| class Foo4(float): |
| def __float__(self): |
| return 42 |
| |
| # Issue 5759: __float__ not called on str subclasses (though it is on |
| # unicode subclasses). |
| class FooStr(str): |
| def __float__(self): |
| return float(str(self)) + 1 |
| |
| self.assertEqual(float(Foo1()), 42.) |
| self.assertEqual(float(Foo2()), 42.) |
| with self.assertWarns(DeprecationWarning): |
| self.assertEqual(float(Foo3(21)), 42.) |
| self.assertRaises(TypeError, float, Foo4(42)) |
| self.assertEqual(float(FooStr('8')), 9.) |
| |
| class Foo5: |
| def __float__(self): |
| return "" |
| self.assertRaises(TypeError, time.sleep, Foo5()) |
| |
| # Issue #24731 |
| class F: |
| def __float__(self): |
| return OtherFloatSubclass(42.) |
| with self.assertWarns(DeprecationWarning): |
| self.assertEqual(float(F()), 42.) |
| with self.assertWarns(DeprecationWarning): |
| self.assertIs(type(float(F())), float) |
| with self.assertWarns(DeprecationWarning): |
| self.assertEqual(FloatSubclass(F()), 42.) |
| with self.assertWarns(DeprecationWarning): |
| self.assertIs(type(FloatSubclass(F())), FloatSubclass) |
| |
| def test_keyword_args(self): |
| with self.assertRaisesRegex(TypeError, 'keyword argument'): |
| float(x='3.14') |
| |
| def test_is_integer(self): |
| self.assertFalse((1.1).is_integer()) |
| self.assertTrue((1.).is_integer()) |
| self.assertFalse(float("nan").is_integer()) |
| self.assertFalse(float("inf").is_integer()) |
| |
| def test_floatasratio(self): |
| for f, ratio in [ |
| (0.875, (7, 8)), |
| (-0.875, (-7, 8)), |
| (0.0, (0, 1)), |
| (11.5, (23, 2)), |
| ]: |
| self.assertEqual(f.as_integer_ratio(), ratio) |
| |
| for i in range(10000): |
| f = random.random() |
| f *= 10 ** random.randint(-100, 100) |
| n, d = f.as_integer_ratio() |
| self.assertEqual(float(n).__truediv__(d), f) |
| |
| R = fractions.Fraction |
| self.assertEqual(R(0, 1), |
| R(*float(0.0).as_integer_ratio())) |
| self.assertEqual(R(5, 2), |
| R(*float(2.5).as_integer_ratio())) |
| self.assertEqual(R(1, 2), |
| R(*float(0.5).as_integer_ratio())) |
| self.assertEqual(R(4728779608739021, 2251799813685248), |
| R(*float(2.1).as_integer_ratio())) |
| self.assertEqual(R(-4728779608739021, 2251799813685248), |
| R(*float(-2.1).as_integer_ratio())) |
| self.assertEqual(R(-2100, 1), |
| R(*float(-2100.0).as_integer_ratio())) |
| |
| self.assertRaises(OverflowError, float('inf').as_integer_ratio) |
| self.assertRaises(OverflowError, float('-inf').as_integer_ratio) |
| self.assertRaises(ValueError, float('nan').as_integer_ratio) |
| |
| def test_float_containment(self): |
| floats = (INF, -INF, 0.0, 1.0, NAN) |
| for f in floats: |
| self.assertIn(f, [f]) |
| self.assertIn(f, (f,)) |
| self.assertIn(f, {f}) |
| self.assertIn(f, {f: None}) |
| self.assertEqual([f].count(f), 1, "[].count('%r') != 1" % f) |
| self.assertIn(f, floats) |
| |
| for f in floats: |
| # nonidentical containers, same type, same contents |
| self.assertTrue([f] == [f], "[%r] != [%r]" % (f, f)) |
| self.assertTrue((f,) == (f,), "(%r,) != (%r,)" % (f, f)) |
| self.assertTrue({f} == {f}, "{%r} != {%r}" % (f, f)) |
| self.assertTrue({f : None} == {f: None}, "{%r : None} != " |
| "{%r : None}" % (f, f)) |
| |
| # identical containers |
| l, t, s, d = [f], (f,), {f}, {f: None} |
| self.assertTrue(l == l, "[%r] not equal to itself" % f) |
| self.assertTrue(t == t, "(%r,) not equal to itself" % f) |
| self.assertTrue(s == s, "{%r} not equal to itself" % f) |
| self.assertTrue(d == d, "{%r : None} not equal to itself" % f) |
| |
| def assertEqualAndEqualSign(self, a, b): |
| # fail unless a == b and a and b have the same sign bit; |
| # the only difference from assertEqual is that this test |
| # distinguishes -0.0 and 0.0. |
| self.assertEqual((a, copysign(1.0, a)), (b, copysign(1.0, b))) |
| |
| @support.requires_IEEE_754 |
| def test_float_mod(self): |
| # Check behaviour of % operator for IEEE 754 special cases. |
| # In particular, check signs of zeros. |
| mod = operator.mod |
| |
| self.assertEqualAndEqualSign(mod(-1.0, 1.0), 0.0) |
| self.assertEqualAndEqualSign(mod(-1e-100, 1.0), 1.0) |
| self.assertEqualAndEqualSign(mod(-0.0, 1.0), 0.0) |
| self.assertEqualAndEqualSign(mod(0.0, 1.0), 0.0) |
| self.assertEqualAndEqualSign(mod(1e-100, 1.0), 1e-100) |
| self.assertEqualAndEqualSign(mod(1.0, 1.0), 0.0) |
| |
| self.assertEqualAndEqualSign(mod(-1.0, -1.0), -0.0) |
| self.assertEqualAndEqualSign(mod(-1e-100, -1.0), -1e-100) |
| self.assertEqualAndEqualSign(mod(-0.0, -1.0), -0.0) |
| self.assertEqualAndEqualSign(mod(0.0, -1.0), -0.0) |
| self.assertEqualAndEqualSign(mod(1e-100, -1.0), -1.0) |
| self.assertEqualAndEqualSign(mod(1.0, -1.0), -0.0) |
| |
| @support.requires_IEEE_754 |
| def test_float_pow(self): |
| # test builtin pow and ** operator for IEEE 754 special cases. |
| # Special cases taken from section F.9.4.4 of the C99 specification |
| |
| for pow_op in pow, operator.pow: |
| # x**NAN is NAN for any x except 1 |
| self.assertTrue(isnan(pow_op(-INF, NAN))) |
| self.assertTrue(isnan(pow_op(-2.0, NAN))) |
| self.assertTrue(isnan(pow_op(-1.0, NAN))) |
| self.assertTrue(isnan(pow_op(-0.5, NAN))) |
| self.assertTrue(isnan(pow_op(-0.0, NAN))) |
| self.assertTrue(isnan(pow_op(0.0, NAN))) |
| self.assertTrue(isnan(pow_op(0.5, NAN))) |
| self.assertTrue(isnan(pow_op(2.0, NAN))) |
| self.assertTrue(isnan(pow_op(INF, NAN))) |
| self.assertTrue(isnan(pow_op(NAN, NAN))) |
| |
| # NAN**y is NAN for any y except +-0 |
| self.assertTrue(isnan(pow_op(NAN, -INF))) |
| self.assertTrue(isnan(pow_op(NAN, -2.0))) |
| self.assertTrue(isnan(pow_op(NAN, -1.0))) |
| self.assertTrue(isnan(pow_op(NAN, -0.5))) |
| self.assertTrue(isnan(pow_op(NAN, 0.5))) |
| self.assertTrue(isnan(pow_op(NAN, 1.0))) |
| self.assertTrue(isnan(pow_op(NAN, 2.0))) |
| self.assertTrue(isnan(pow_op(NAN, INF))) |
| |
| # (+-0)**y raises ZeroDivisionError for y a negative odd integer |
| self.assertRaises(ZeroDivisionError, pow_op, -0.0, -1.0) |
| self.assertRaises(ZeroDivisionError, pow_op, 0.0, -1.0) |
| |
| # (+-0)**y raises ZeroDivisionError for y finite and negative |
| # but not an odd integer |
| self.assertRaises(ZeroDivisionError, pow_op, -0.0, -2.0) |
| self.assertRaises(ZeroDivisionError, pow_op, -0.0, -0.5) |
| self.assertRaises(ZeroDivisionError, pow_op, 0.0, -2.0) |
| self.assertRaises(ZeroDivisionError, pow_op, 0.0, -0.5) |
| |
| # (+-0)**y is +-0 for y a positive odd integer |
| self.assertEqualAndEqualSign(pow_op(-0.0, 1.0), -0.0) |
| self.assertEqualAndEqualSign(pow_op(0.0, 1.0), 0.0) |
| |
| # (+-0)**y is 0 for y finite and positive but not an odd integer |
| self.assertEqualAndEqualSign(pow_op(-0.0, 0.5), 0.0) |
| self.assertEqualAndEqualSign(pow_op(-0.0, 2.0), 0.0) |
| self.assertEqualAndEqualSign(pow_op(0.0, 0.5), 0.0) |
| self.assertEqualAndEqualSign(pow_op(0.0, 2.0), 0.0) |
| |
| # (-1)**+-inf is 1 |
| self.assertEqualAndEqualSign(pow_op(-1.0, -INF), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, INF), 1.0) |
| |
| # 1**y is 1 for any y, even if y is an infinity or nan |
| self.assertEqualAndEqualSign(pow_op(1.0, -INF), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, -2.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, -1.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, -0.5), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, 0.5), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, 1.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, 2.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, INF), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, NAN), 1.0) |
| |
| # x**+-0 is 1 for any x, even if x is a zero, infinity, or nan |
| self.assertEqualAndEqualSign(pow_op(-INF, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-0.5, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-0.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(0.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(0.5, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(INF, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(NAN, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-INF, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-0.5, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-0.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(0.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(0.5, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(INF, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(NAN, -0.0), 1.0) |
| |
| # x**y defers to complex pow for finite negative x and |
| # non-integral y. |
| self.assertEqual(type(pow_op(-2.0, -0.5)), complex) |
| self.assertEqual(type(pow_op(-2.0, 0.5)), complex) |
| self.assertEqual(type(pow_op(-1.0, -0.5)), complex) |
| self.assertEqual(type(pow_op(-1.0, 0.5)), complex) |
| self.assertEqual(type(pow_op(-0.5, -0.5)), complex) |
| self.assertEqual(type(pow_op(-0.5, 0.5)), complex) |
| |
| # x**-INF is INF for abs(x) < 1 |
| self.assertEqualAndEqualSign(pow_op(-0.5, -INF), INF) |
| self.assertEqualAndEqualSign(pow_op(-0.0, -INF), INF) |
| self.assertEqualAndEqualSign(pow_op(0.0, -INF), INF) |
| self.assertEqualAndEqualSign(pow_op(0.5, -INF), INF) |
| |
| # x**-INF is 0 for abs(x) > 1 |
| self.assertEqualAndEqualSign(pow_op(-INF, -INF), 0.0) |
| self.assertEqualAndEqualSign(pow_op(-2.0, -INF), 0.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, -INF), 0.0) |
| self.assertEqualAndEqualSign(pow_op(INF, -INF), 0.0) |
| |
| # x**INF is 0 for abs(x) < 1 |
| self.assertEqualAndEqualSign(pow_op(-0.5, INF), 0.0) |
| self.assertEqualAndEqualSign(pow_op(-0.0, INF), 0.0) |
| self.assertEqualAndEqualSign(pow_op(0.0, INF), 0.0) |
| self.assertEqualAndEqualSign(pow_op(0.5, INF), 0.0) |
| |
| # x**INF is INF for abs(x) > 1 |
| self.assertEqualAndEqualSign(pow_op(-INF, INF), INF) |
| self.assertEqualAndEqualSign(pow_op(-2.0, INF), INF) |
| self.assertEqualAndEqualSign(pow_op(2.0, INF), INF) |
| self.assertEqualAndEqualSign(pow_op(INF, INF), INF) |
| |
| # (-INF)**y is -0.0 for y a negative odd integer |
| self.assertEqualAndEqualSign(pow_op(-INF, -1.0), -0.0) |
| |
| # (-INF)**y is 0.0 for y negative but not an odd integer |
| self.assertEqualAndEqualSign(pow_op(-INF, -0.5), 0.0) |
| self.assertEqualAndEqualSign(pow_op(-INF, -2.0), 0.0) |
| |
| # (-INF)**y is -INF for y a positive odd integer |
| self.assertEqualAndEqualSign(pow_op(-INF, 1.0), -INF) |
| |
| # (-INF)**y is INF for y positive but not an odd integer |
| self.assertEqualAndEqualSign(pow_op(-INF, 0.5), INF) |
| self.assertEqualAndEqualSign(pow_op(-INF, 2.0), INF) |
| |
| # INF**y is INF for y positive |
| self.assertEqualAndEqualSign(pow_op(INF, 0.5), INF) |
| self.assertEqualAndEqualSign(pow_op(INF, 1.0), INF) |
| self.assertEqualAndEqualSign(pow_op(INF, 2.0), INF) |
| |
| # INF**y is 0.0 for y negative |
| self.assertEqualAndEqualSign(pow_op(INF, -2.0), 0.0) |
| self.assertEqualAndEqualSign(pow_op(INF, -1.0), 0.0) |
| self.assertEqualAndEqualSign(pow_op(INF, -0.5), 0.0) |
| |
| # basic checks not covered by the special cases above |
| self.assertEqualAndEqualSign(pow_op(-2.0, -2.0), 0.25) |
| self.assertEqualAndEqualSign(pow_op(-2.0, -1.0), -0.5) |
| self.assertEqualAndEqualSign(pow_op(-2.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-2.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-2.0, 1.0), -2.0) |
| self.assertEqualAndEqualSign(pow_op(-2.0, 2.0), 4.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, -2.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, -1.0), -1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, 1.0), -1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, 2.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, -2.0), 0.25) |
| self.assertEqualAndEqualSign(pow_op(2.0, -1.0), 0.5) |
| self.assertEqualAndEqualSign(pow_op(2.0, -0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, 0.0), 1.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, 1.0), 2.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, 2.0), 4.0) |
| |
| # 1 ** large and -1 ** large; some libms apparently |
| # have problems with these |
| self.assertEqualAndEqualSign(pow_op(1.0, -1e100), 1.0) |
| self.assertEqualAndEqualSign(pow_op(1.0, 1e100), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, -1e100), 1.0) |
| self.assertEqualAndEqualSign(pow_op(-1.0, 1e100), 1.0) |
| |
| # check sign for results that underflow to 0 |
| self.assertEqualAndEqualSign(pow_op(-2.0, -2000.0), 0.0) |
| self.assertEqual(type(pow_op(-2.0, -2000.5)), complex) |
| self.assertEqualAndEqualSign(pow_op(-2.0, -2001.0), -0.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, -2000.0), 0.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, -2000.5), 0.0) |
| self.assertEqualAndEqualSign(pow_op(2.0, -2001.0), 0.0) |
| self.assertEqualAndEqualSign(pow_op(-0.5, 2000.0), 0.0) |
| self.assertEqual(type(pow_op(-0.5, 2000.5)), complex) |
| self.assertEqualAndEqualSign(pow_op(-0.5, 2001.0), -0.0) |
| self.assertEqualAndEqualSign(pow_op(0.5, 2000.0), 0.0) |
| self.assertEqualAndEqualSign(pow_op(0.5, 2000.5), 0.0) |
| self.assertEqualAndEqualSign(pow_op(0.5, 2001.0), 0.0) |
| |
| # check we don't raise an exception for subnormal results, |
| # and validate signs. Tests currently disabled, since |
| # they fail on systems where a subnormal result from pow |
| # is flushed to zero (e.g. Debian/ia64.) |
| #self.assertTrue(0.0 < pow_op(0.5, 1048) < 1e-315) |
| #self.assertTrue(0.0 < pow_op(-0.5, 1048) < 1e-315) |
| #self.assertTrue(0.0 < pow_op(0.5, 1047) < 1e-315) |
| #self.assertTrue(0.0 > pow_op(-0.5, 1047) > -1e-315) |
| #self.assertTrue(0.0 < pow_op(2.0, -1048) < 1e-315) |
| #self.assertTrue(0.0 < pow_op(-2.0, -1048) < 1e-315) |
| #self.assertTrue(0.0 < pow_op(2.0, -1047) < 1e-315) |
| #self.assertTrue(0.0 > pow_op(-2.0, -1047) > -1e-315) |
| |
| |
| @requires_setformat |
| class FormatFunctionsTestCase(unittest.TestCase): |
| |
| def setUp(self): |
| self.save_formats = {'double':float.__getformat__('double'), |
| 'float':float.__getformat__('float')} |
| |
| def tearDown(self): |
| float.__setformat__('double', self.save_formats['double']) |
| float.__setformat__('float', self.save_formats['float']) |
| |
| def test_getformat(self): |
| self.assertIn(float.__getformat__('double'), |
| ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) |
| self.assertIn(float.__getformat__('float'), |
| ['unknown', 'IEEE, big-endian', 'IEEE, little-endian']) |
| self.assertRaises(ValueError, float.__getformat__, 'chicken') |
| self.assertRaises(TypeError, float.__getformat__, 1) |
| |
| def test_setformat(self): |
| for t in 'double', 'float': |
| float.__setformat__(t, 'unknown') |
| if self.save_formats[t] == 'IEEE, big-endian': |
| self.assertRaises(ValueError, float.__setformat__, |
| t, 'IEEE, little-endian') |
| elif self.save_formats[t] == 'IEEE, little-endian': |
| self.assertRaises(ValueError, float.__setformat__, |
| t, 'IEEE, big-endian') |
| else: |
| self.assertRaises(ValueError, float.__setformat__, |
| t, 'IEEE, big-endian') |
| self.assertRaises(ValueError, float.__setformat__, |
| t, 'IEEE, little-endian') |
| self.assertRaises(ValueError, float.__setformat__, |
| t, 'chicken') |
| self.assertRaises(ValueError, float.__setformat__, |
| 'chicken', 'unknown') |
| |
| BE_DOUBLE_INF = b'\x7f\xf0\x00\x00\x00\x00\x00\x00' |
| LE_DOUBLE_INF = bytes(reversed(BE_DOUBLE_INF)) |
| BE_DOUBLE_NAN = b'\x7f\xf8\x00\x00\x00\x00\x00\x00' |
| LE_DOUBLE_NAN = bytes(reversed(BE_DOUBLE_NAN)) |
| |
| BE_FLOAT_INF = b'\x7f\x80\x00\x00' |
| LE_FLOAT_INF = bytes(reversed(BE_FLOAT_INF)) |
| BE_FLOAT_NAN = b'\x7f\xc0\x00\x00' |
| LE_FLOAT_NAN = bytes(reversed(BE_FLOAT_NAN)) |
| |
| # on non-IEEE platforms, attempting to unpack a bit pattern |
| # representing an infinity or a NaN should raise an exception. |
| |
| @requires_setformat |
| class UnknownFormatTestCase(unittest.TestCase): |
| def setUp(self): |
| self.save_formats = {'double':float.__getformat__('double'), |
| 'float':float.__getformat__('float')} |
| float.__setformat__('double', 'unknown') |
| float.__setformat__('float', 'unknown') |
| |
| def tearDown(self): |
| float.__setformat__('double', self.save_formats['double']) |
| float.__setformat__('float', self.save_formats['float']) |
| |
| def test_double_specials_dont_unpack(self): |
| for fmt, data in [('>d', BE_DOUBLE_INF), |
| ('>d', BE_DOUBLE_NAN), |
| ('<d', LE_DOUBLE_INF), |
| ('<d', LE_DOUBLE_NAN)]: |
| self.assertRaises(ValueError, struct.unpack, fmt, data) |
| |
| def test_float_specials_dont_unpack(self): |
| for fmt, data in [('>f', BE_FLOAT_INF), |
| ('>f', BE_FLOAT_NAN), |
| ('<f', LE_FLOAT_INF), |
| ('<f', LE_FLOAT_NAN)]: |
| self.assertRaises(ValueError, struct.unpack, fmt, data) |
| |
| |
| # on an IEEE platform, all we guarantee is that bit patterns |
| # representing infinities or NaNs do not raise an exception; all else |
| # is accident (today). |
| # let's also try to guarantee that -0.0 and 0.0 don't get confused. |
| |
| class IEEEFormatTestCase(unittest.TestCase): |
| |
| @support.requires_IEEE_754 |
| def test_double_specials_do_unpack(self): |
| for fmt, data in [('>d', BE_DOUBLE_INF), |
| ('>d', BE_DOUBLE_NAN), |
| ('<d', LE_DOUBLE_INF), |
| ('<d', LE_DOUBLE_NAN)]: |
| struct.unpack(fmt, data) |
| |
| @support.requires_IEEE_754 |
| def test_float_specials_do_unpack(self): |
| for fmt, data in [('>f', BE_FLOAT_INF), |
| ('>f', BE_FLOAT_NAN), |
| ('<f', LE_FLOAT_INF), |
| ('<f', LE_FLOAT_NAN)]: |
| struct.unpack(fmt, data) |
| |
| @support.requires_IEEE_754 |
| def test_serialized_float_rounding(self): |
| from _testcapi import FLT_MAX |
| self.assertEqual(struct.pack("<f", 3.40282356e38), struct.pack("<f", FLT_MAX)) |
| self.assertEqual(struct.pack("<f", -3.40282356e38), struct.pack("<f", -FLT_MAX)) |
| |
| class FormatTestCase(unittest.TestCase): |
| |
| def test_format(self): |
| # these should be rewritten to use both format(x, spec) and |
| # x.__format__(spec) |
| |
| self.assertEqual(format(0.0, 'f'), '0.000000') |
| |
| # the default is 'g', except for empty format spec |
| self.assertEqual(format(0.0, ''), '0.0') |
| self.assertEqual(format(0.01, ''), '0.01') |
| self.assertEqual(format(0.01, 'g'), '0.01') |
| |
| # empty presentation type should format in the same way as str |
| # (issue 5920) |
| x = 100/7. |
| self.assertEqual(format(x, ''), str(x)) |
| self.assertEqual(format(x, '-'), str(x)) |
| self.assertEqual(format(x, '>'), str(x)) |
| self.assertEqual(format(x, '2'), str(x)) |
| |
| self.assertEqual(format(1.0, 'f'), '1.000000') |
| |
| self.assertEqual(format(-1.0, 'f'), '-1.000000') |
| |
| self.assertEqual(format( 1.0, ' f'), ' 1.000000') |
| self.assertEqual(format(-1.0, ' f'), '-1.000000') |
| self.assertEqual(format( 1.0, '+f'), '+1.000000') |
| self.assertEqual(format(-1.0, '+f'), '-1.000000') |
| |
| # % formatting |
| self.assertEqual(format(-1.0, '%'), '-100.000000%') |
| |
| # conversion to string should fail |
| self.assertRaises(ValueError, format, 3.0, "s") |
| |
| # other format specifiers shouldn't work on floats, |
| # in particular int specifiers |
| for format_spec in ([chr(x) for x in range(ord('a'), ord('z')+1)] + |
| [chr(x) for x in range(ord('A'), ord('Z')+1)]): |
| if not format_spec in 'eEfFgGn%': |
| self.assertRaises(ValueError, format, 0.0, format_spec) |
| self.assertRaises(ValueError, format, 1.0, format_spec) |
| self.assertRaises(ValueError, format, -1.0, format_spec) |
| self.assertRaises(ValueError, format, 1e100, format_spec) |
| self.assertRaises(ValueError, format, -1e100, format_spec) |
| self.assertRaises(ValueError, format, 1e-100, format_spec) |
| self.assertRaises(ValueError, format, -1e-100, format_spec) |
| |
| # issue 3382 |
| self.assertEqual(format(NAN, 'f'), 'nan') |
| self.assertEqual(format(NAN, 'F'), 'NAN') |
| self.assertEqual(format(INF, 'f'), 'inf') |
| self.assertEqual(format(INF, 'F'), 'INF') |
| |
| @support.requires_IEEE_754 |
| def test_format_testfile(self): |
| with open(format_testfile) as testfile: |
| for line in testfile: |
| if line.startswith('--'): |
| continue |
| line = line.strip() |
| if not line: |
| continue |
| |
| lhs, rhs = map(str.strip, line.split('->')) |
| fmt, arg = lhs.split() |
| self.assertEqual(fmt % float(arg), rhs) |
| self.assertEqual(fmt % -float(arg), '-' + rhs) |
| |
| def test_issue5864(self): |
| self.assertEqual(format(123.456, '.4'), '123.5') |
| self.assertEqual(format(1234.56, '.4'), '1.235e+03') |
| self.assertEqual(format(12345.6, '.4'), '1.235e+04') |
| |
| class ReprTestCase(unittest.TestCase): |
| def test_repr(self): |
| floats_file = open(os.path.join(os.path.split(__file__)[0], |
| 'floating_points.txt')) |
| for line in floats_file: |
| line = line.strip() |
| if not line or line.startswith('#'): |
| continue |
| v = eval(line) |
| self.assertEqual(v, eval(repr(v))) |
| floats_file.close() |
| |
| @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', |
| "applies only when using short float repr style") |
| def test_short_repr(self): |
| # test short float repr introduced in Python 3.1. One aspect |
| # of this repr is that we get some degree of str -> float -> |
| # str roundtripping. In particular, for any numeric string |
| # containing 15 or fewer significant digits, those exact same |
| # digits (modulo trailing zeros) should appear in the output. |
| # No more repr(0.03) -> "0.029999999999999999"! |
| |
| test_strings = [ |
| # output always includes *either* a decimal point and at |
| # least one digit after that point, or an exponent. |
| '0.0', |
| '1.0', |
| '0.01', |
| '0.02', |
| '0.03', |
| '0.04', |
| '0.05', |
| '1.23456789', |
| '10.0', |
| '100.0', |
| # values >= 1e16 get an exponent... |
| '1000000000000000.0', |
| '9999999999999990.0', |
| '1e+16', |
| '1e+17', |
| # ... and so do values < 1e-4 |
| '0.001', |
| '0.001001', |
| '0.00010000000000001', |
| '0.0001', |
| '9.999999999999e-05', |
| '1e-05', |
| # values designed to provoke failure if the FPU rounding |
| # precision isn't set correctly |
| '8.72293771110361e+25', |
| '7.47005307342313e+26', |
| '2.86438000439698e+28', |
| '8.89142905246179e+28', |
| '3.08578087079232e+35', |
| ] |
| |
| for s in test_strings: |
| negs = '-'+s |
| self.assertEqual(s, repr(float(s))) |
| self.assertEqual(negs, repr(float(negs))) |
| # Since Python 3.2, repr and str are identical |
| self.assertEqual(repr(float(s)), str(float(s))) |
| self.assertEqual(repr(float(negs)), str(float(negs))) |
| |
| @support.requires_IEEE_754 |
| class RoundTestCase(unittest.TestCase): |
| |
| def test_inf_nan(self): |
| self.assertRaises(OverflowError, round, INF) |
| self.assertRaises(OverflowError, round, -INF) |
| self.assertRaises(ValueError, round, NAN) |
| self.assertRaises(TypeError, round, INF, 0.0) |
| self.assertRaises(TypeError, round, -INF, 1.0) |
| self.assertRaises(TypeError, round, NAN, "ceci n'est pas un integer") |
| self.assertRaises(TypeError, round, -0.0, 1j) |
| |
| def test_large_n(self): |
| for n in [324, 325, 400, 2**31-1, 2**31, 2**32, 2**100]: |
| self.assertEqual(round(123.456, n), 123.456) |
| self.assertEqual(round(-123.456, n), -123.456) |
| self.assertEqual(round(1e300, n), 1e300) |
| self.assertEqual(round(1e-320, n), 1e-320) |
| self.assertEqual(round(1e150, 300), 1e150) |
| self.assertEqual(round(1e300, 307), 1e300) |
| self.assertEqual(round(-3.1415, 308), -3.1415) |
| self.assertEqual(round(1e150, 309), 1e150) |
| self.assertEqual(round(1.4e-315, 315), 1e-315) |
| |
| def test_small_n(self): |
| for n in [-308, -309, -400, 1-2**31, -2**31, -2**31-1, -2**100]: |
| self.assertEqual(round(123.456, n), 0.0) |
| self.assertEqual(round(-123.456, n), -0.0) |
| self.assertEqual(round(1e300, n), 0.0) |
| self.assertEqual(round(1e-320, n), 0.0) |
| |
| def test_overflow(self): |
| self.assertRaises(OverflowError, round, 1.6e308, -308) |
| self.assertRaises(OverflowError, round, -1.7e308, -308) |
| |
| @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', |
| "applies only when using short float repr style") |
| def test_previous_round_bugs(self): |
| # particular cases that have occurred in bug reports |
| self.assertEqual(round(562949953421312.5, 1), |
| 562949953421312.5) |
| self.assertEqual(round(56294995342131.5, 3), |
| 56294995342131.5) |
| # round-half-even |
| self.assertEqual(round(25.0, -1), 20.0) |
| self.assertEqual(round(35.0, -1), 40.0) |
| self.assertEqual(round(45.0, -1), 40.0) |
| self.assertEqual(round(55.0, -1), 60.0) |
| self.assertEqual(round(65.0, -1), 60.0) |
| self.assertEqual(round(75.0, -1), 80.0) |
| self.assertEqual(round(85.0, -1), 80.0) |
| self.assertEqual(round(95.0, -1), 100.0) |
| |
| @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', |
| "applies only when using short float repr style") |
| def test_matches_float_format(self): |
| # round should give the same results as float formatting |
| for i in range(500): |
| x = i/1000. |
| self.assertEqual(float(format(x, '.0f')), round(x, 0)) |
| self.assertEqual(float(format(x, '.1f')), round(x, 1)) |
| self.assertEqual(float(format(x, '.2f')), round(x, 2)) |
| self.assertEqual(float(format(x, '.3f')), round(x, 3)) |
| |
| for i in range(5, 5000, 10): |
| x = i/1000. |
| self.assertEqual(float(format(x, '.0f')), round(x, 0)) |
| self.assertEqual(float(format(x, '.1f')), round(x, 1)) |
| self.assertEqual(float(format(x, '.2f')), round(x, 2)) |
| self.assertEqual(float(format(x, '.3f')), round(x, 3)) |
| |
| for i in range(500): |
| x = random.random() |
| self.assertEqual(float(format(x, '.0f')), round(x, 0)) |
| self.assertEqual(float(format(x, '.1f')), round(x, 1)) |
| self.assertEqual(float(format(x, '.2f')), round(x, 2)) |
| self.assertEqual(float(format(x, '.3f')), round(x, 3)) |
| |
| def test_format_specials(self): |
| # Test formatting of nans and infs. |
| |
| def test(fmt, value, expected): |
| # Test with both % and format(). |
| self.assertEqual(fmt % value, expected, fmt) |
| fmt = fmt[1:] # strip off the % |
| self.assertEqual(format(value, fmt), expected, fmt) |
| |
| for fmt in ['%e', '%f', '%g', '%.0e', '%.6f', '%.20g', |
| '%#e', '%#f', '%#g', '%#.20e', '%#.15f', '%#.3g']: |
| pfmt = '%+' + fmt[1:] |
| sfmt = '% ' + fmt[1:] |
| test(fmt, INF, 'inf') |
| test(fmt, -INF, '-inf') |
| test(fmt, NAN, 'nan') |
| test(fmt, -NAN, 'nan') |
| # When asking for a sign, it's always provided. nans are |
| # always positive. |
| test(pfmt, INF, '+inf') |
| test(pfmt, -INF, '-inf') |
| test(pfmt, NAN, '+nan') |
| test(pfmt, -NAN, '+nan') |
| # When using ' ' for a sign code, only infs can be negative. |
| # Others have a space. |
| test(sfmt, INF, ' inf') |
| test(sfmt, -INF, '-inf') |
| test(sfmt, NAN, ' nan') |
| test(sfmt, -NAN, ' nan') |
| |
| def test_None_ndigits(self): |
| for x in round(1.23), round(1.23, None), round(1.23, ndigits=None): |
| self.assertEqual(x, 1) |
| self.assertIsInstance(x, int) |
| for x in round(1.78), round(1.78, None), round(1.78, ndigits=None): |
| self.assertEqual(x, 2) |
| self.assertIsInstance(x, int) |
| |
| |
| # Beginning with Python 2.6 float has cross platform compatible |
| # ways to create and represent inf and nan |
| class InfNanTest(unittest.TestCase): |
| def test_inf_from_str(self): |
| self.assertTrue(isinf(float("inf"))) |
| self.assertTrue(isinf(float("+inf"))) |
| self.assertTrue(isinf(float("-inf"))) |
| self.assertTrue(isinf(float("infinity"))) |
| self.assertTrue(isinf(float("+infinity"))) |
| self.assertTrue(isinf(float("-infinity"))) |
| |
| self.assertEqual(repr(float("inf")), "inf") |
| self.assertEqual(repr(float("+inf")), "inf") |
| self.assertEqual(repr(float("-inf")), "-inf") |
| self.assertEqual(repr(float("infinity")), "inf") |
| self.assertEqual(repr(float("+infinity")), "inf") |
| self.assertEqual(repr(float("-infinity")), "-inf") |
| |
| self.assertEqual(repr(float("INF")), "inf") |
| self.assertEqual(repr(float("+Inf")), "inf") |
| self.assertEqual(repr(float("-iNF")), "-inf") |
| self.assertEqual(repr(float("Infinity")), "inf") |
| self.assertEqual(repr(float("+iNfInItY")), "inf") |
| self.assertEqual(repr(float("-INFINITY")), "-inf") |
| |
| self.assertEqual(str(float("inf")), "inf") |
| self.assertEqual(str(float("+inf")), "inf") |
| self.assertEqual(str(float("-inf")), "-inf") |
| self.assertEqual(str(float("infinity")), "inf") |
| self.assertEqual(str(float("+infinity")), "inf") |
| self.assertEqual(str(float("-infinity")), "-inf") |
| |
| self.assertRaises(ValueError, float, "info") |
| self.assertRaises(ValueError, float, "+info") |
| self.assertRaises(ValueError, float, "-info") |
| self.assertRaises(ValueError, float, "in") |
| self.assertRaises(ValueError, float, "+in") |
| self.assertRaises(ValueError, float, "-in") |
| self.assertRaises(ValueError, float, "infinit") |
| self.assertRaises(ValueError, float, "+Infin") |
| self.assertRaises(ValueError, float, "-INFI") |
| self.assertRaises(ValueError, float, "infinitys") |
| |
| self.assertRaises(ValueError, float, "++Inf") |
| self.assertRaises(ValueError, float, "-+inf") |
| self.assertRaises(ValueError, float, "+-infinity") |
| self.assertRaises(ValueError, float, "--Infinity") |
| |
| def test_inf_as_str(self): |
| self.assertEqual(repr(1e300 * 1e300), "inf") |
| self.assertEqual(repr(-1e300 * 1e300), "-inf") |
| |
| self.assertEqual(str(1e300 * 1e300), "inf") |
| self.assertEqual(str(-1e300 * 1e300), "-inf") |
| |
| def test_nan_from_str(self): |
| self.assertTrue(isnan(float("nan"))) |
| self.assertTrue(isnan(float("+nan"))) |
| self.assertTrue(isnan(float("-nan"))) |
| |
| self.assertEqual(repr(float("nan")), "nan") |
| self.assertEqual(repr(float("+nan")), "nan") |
| self.assertEqual(repr(float("-nan")), "nan") |
| |
| self.assertEqual(repr(float("NAN")), "nan") |
| self.assertEqual(repr(float("+NAn")), "nan") |
| self.assertEqual(repr(float("-NaN")), "nan") |
| |
| self.assertEqual(str(float("nan")), "nan") |
| self.assertEqual(str(float("+nan")), "nan") |
| self.assertEqual(str(float("-nan")), "nan") |
| |
| self.assertRaises(ValueError, float, "nana") |
| self.assertRaises(ValueError, float, "+nana") |
| self.assertRaises(ValueError, float, "-nana") |
| self.assertRaises(ValueError, float, "na") |
| self.assertRaises(ValueError, float, "+na") |
| self.assertRaises(ValueError, float, "-na") |
| |
| self.assertRaises(ValueError, float, "++nan") |
| self.assertRaises(ValueError, float, "-+NAN") |
| self.assertRaises(ValueError, float, "+-NaN") |
| self.assertRaises(ValueError, float, "--nAn") |
| |
| def test_nan_as_str(self): |
| self.assertEqual(repr(1e300 * 1e300 * 0), "nan") |
| self.assertEqual(repr(-1e300 * 1e300 * 0), "nan") |
| |
| self.assertEqual(str(1e300 * 1e300 * 0), "nan") |
| self.assertEqual(str(-1e300 * 1e300 * 0), "nan") |
| |
| def test_inf_signs(self): |
| self.assertEqual(copysign(1.0, float('inf')), 1.0) |
| self.assertEqual(copysign(1.0, float('-inf')), -1.0) |
| |
| @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', |
| "applies only when using short float repr style") |
| def test_nan_signs(self): |
| # When using the dtoa.c code, the sign of float('nan') should |
| # be predictable. |
| self.assertEqual(copysign(1.0, float('nan')), 1.0) |
| self.assertEqual(copysign(1.0, float('-nan')), -1.0) |
| |
| |
| fromHex = float.fromhex |
| toHex = float.hex |
| class HexFloatTestCase(unittest.TestCase): |
| MAX = fromHex('0x.fffffffffffff8p+1024') # max normal |
| MIN = fromHex('0x1p-1022') # min normal |
| TINY = fromHex('0x0.0000000000001p-1022') # min subnormal |
| EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up |
| |
| def identical(self, x, y): |
| # check that floats x and y are identical, or that both |
| # are NaNs |
| if isnan(x) or isnan(y): |
| if isnan(x) == isnan(y): |
| return |
| elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)): |
| return |
| self.fail('%r not identical to %r' % (x, y)) |
| |
| def test_ends(self): |
| self.identical(self.MIN, ldexp(1.0, -1022)) |
| self.identical(self.TINY, ldexp(1.0, -1074)) |
| self.identical(self.EPS, ldexp(1.0, -52)) |
| self.identical(self.MAX, 2.*(ldexp(1.0, 1023) - ldexp(1.0, 970))) |
| |
| def test_invalid_inputs(self): |
| invalid_inputs = [ |
| 'infi', # misspelt infinities and nans |
| '-Infinit', |
| '++inf', |
| '-+Inf', |
| '--nan', |
| '+-NaN', |
| 'snan', |
| 'NaNs', |
| 'nna', |
| 'an', |
| 'nf', |
| 'nfinity', |
| 'inity', |
| 'iinity', |
| '0xnan', |
| '', |
| ' ', |
| 'x1.0p0', |
| '0xX1.0p0', |
| '+ 0x1.0p0', # internal whitespace |
| '- 0x1.0p0', |
| '0 x1.0p0', |
| '0x 1.0p0', |
| '0x1 2.0p0', |
| '+0x1 .0p0', |
| '0x1. 0p0', |
| '-0x1.0 1p0', |
| '-0x1.0 p0', |
| '+0x1.0p +0', |
| '0x1.0p -0', |
| '0x1.0p 0', |
| '+0x1.0p+ 0', |
| '-0x1.0p- 0', |
| '++0x1.0p-0', # double signs |
| '--0x1.0p0', |
| '+-0x1.0p+0', |
| '-+0x1.0p0', |
| '0x1.0p++0', |
| '+0x1.0p+-0', |
| '-0x1.0p-+0', |
| '0x1.0p--0', |
| '0x1.0.p0', |
| '0x.p0', # no hex digits before or after point |
| '0x1,p0', # wrong decimal point character |
| '0x1pa', |
| '0x1p\uff10', # fullwidth Unicode digits |
| '\uff10x1p0', |
| '0x\uff11p0', |
| '0x1.\uff10p0', |
| '0x1p0 \n 0x2p0', |
| '0x1p0\0 0x1p0', # embedded null byte is not end of string |
| ] |
| for x in invalid_inputs: |
| try: |
| result = fromHex(x) |
| except ValueError: |
| pass |
| else: |
| self.fail('Expected float.fromhex(%r) to raise ValueError; ' |
| 'got %r instead' % (x, result)) |
| |
| |
| def test_whitespace(self): |
| value_pairs = [ |
| ('inf', INF), |
| ('-Infinity', -INF), |
| ('nan', NAN), |
| ('1.0', 1.0), |
| ('-0x.2', -0.125), |
| ('-0.0', -0.0) |
| ] |
| whitespace = [ |
| '', |
| ' ', |
| '\t', |
| '\n', |
| '\n \t', |
| '\f', |
| '\v', |
| '\r' |
| ] |
| for inp, expected in value_pairs: |
| for lead in whitespace: |
| for trail in whitespace: |
| got = fromHex(lead + inp + trail) |
| self.identical(got, expected) |
| |
| |
| def test_from_hex(self): |
| MIN = self.MIN; |
| MAX = self.MAX; |
| TINY = self.TINY; |
| EPS = self.EPS; |
| |
| # two spellings of infinity, with optional signs; case-insensitive |
| self.identical(fromHex('inf'), INF) |
| self.identical(fromHex('+Inf'), INF) |
| self.identical(fromHex('-INF'), -INF) |
| self.identical(fromHex('iNf'), INF) |
| self.identical(fromHex('Infinity'), INF) |
| self.identical(fromHex('+INFINITY'), INF) |
| self.identical(fromHex('-infinity'), -INF) |
| self.identical(fromHex('-iNFiNitY'), -INF) |
| |
| # nans with optional sign; case insensitive |
| self.identical(fromHex('nan'), NAN) |
| self.identical(fromHex('+NaN'), NAN) |
| self.identical(fromHex('-NaN'), NAN) |
| self.identical(fromHex('-nAN'), NAN) |
| |
| # variations in input format |
| self.identical(fromHex('1'), 1.0) |
| self.identical(fromHex('+1'), 1.0) |
| self.identical(fromHex('1.'), 1.0) |
| self.identical(fromHex('1.0'), 1.0) |
| self.identical(fromHex('1.0p0'), 1.0) |
| self.identical(fromHex('01'), 1.0) |
| self.identical(fromHex('01.'), 1.0) |
| self.identical(fromHex('0x1'), 1.0) |
| self.identical(fromHex('0x1.'), 1.0) |
| self.identical(fromHex('0x1.0'), 1.0) |
| self.identical(fromHex('+0x1.0'), 1.0) |
| self.identical(fromHex('0x1p0'), 1.0) |
| self.identical(fromHex('0X1p0'), 1.0) |
| self.identical(fromHex('0X1P0'), 1.0) |
| self.identical(fromHex('0x1P0'), 1.0) |
| self.identical(fromHex('0x1.p0'), 1.0) |
| self.identical(fromHex('0x1.0p0'), 1.0) |
| self.identical(fromHex('0x.1p4'), 1.0) |
| self.identical(fromHex('0x.1p04'), 1.0) |
| self.identical(fromHex('0x.1p004'), 1.0) |
| self.identical(fromHex('0x1p+0'), 1.0) |
| self.identical(fromHex('0x1P-0'), 1.0) |
| self.identical(fromHex('+0x1p0'), 1.0) |
| self.identical(fromHex('0x01p0'), 1.0) |
| self.identical(fromHex('0x1p00'), 1.0) |
| self.identical(fromHex(' 0x1p0 '), 1.0) |
| self.identical(fromHex('\n 0x1p0'), 1.0) |
| self.identical(fromHex('0x1p0 \t'), 1.0) |
| self.identical(fromHex('0xap0'), 10.0) |
| self.identical(fromHex('0xAp0'), 10.0) |
| self.identical(fromHex('0xaP0'), 10.0) |
| self.identical(fromHex('0xAP0'), 10.0) |
| self.identical(fromHex('0xbep0'), 190.0) |
| self.identical(fromHex('0xBep0'), 190.0) |
| self.identical(fromHex('0xbEp0'), 190.0) |
| self.identical(fromHex('0XBE0P-4'), 190.0) |
| self.identical(fromHex('0xBEp0'), 190.0) |
| self.identical(fromHex('0xB.Ep4'), 190.0) |
| self.identical(fromHex('0x.BEp8'), 190.0) |
| self.identical(fromHex('0x.0BEp12'), 190.0) |
| |
| # moving the point around |
| pi = fromHex('0x1.921fb54442d18p1') |
| self.identical(fromHex('0x.006487ed5110b46p11'), pi) |
| self.identical(fromHex('0x.00c90fdaa22168cp10'), pi) |
| self.identical(fromHex('0x.01921fb54442d18p9'), pi) |
| self.identical(fromHex('0x.03243f6a8885a3p8'), pi) |
| self.identical(fromHex('0x.06487ed5110b46p7'), pi) |
| self.identical(fromHex('0x.0c90fdaa22168cp6'), pi) |
| self.identical(fromHex('0x.1921fb54442d18p5'), pi) |
| self.identical(fromHex('0x.3243f6a8885a3p4'), pi) |
| self.identical(fromHex('0x.6487ed5110b46p3'), pi) |
| self.identical(fromHex('0x.c90fdaa22168cp2'), pi) |
| self.identical(fromHex('0x1.921fb54442d18p1'), pi) |
| self.identical(fromHex('0x3.243f6a8885a3p0'), pi) |
| self.identical(fromHex('0x6.487ed5110b46p-1'), pi) |
| self.identical(fromHex('0xc.90fdaa22168cp-2'), pi) |
| self.identical(fromHex('0x19.21fb54442d18p-3'), pi) |
| self.identical(fromHex('0x32.43f6a8885a3p-4'), pi) |
| self.identical(fromHex('0x64.87ed5110b46p-5'), pi) |
| self.identical(fromHex('0xc9.0fdaa22168cp-6'), pi) |
| self.identical(fromHex('0x192.1fb54442d18p-7'), pi) |
| self.identical(fromHex('0x324.3f6a8885a3p-8'), pi) |
| self.identical(fromHex('0x648.7ed5110b46p-9'), pi) |
| self.identical(fromHex('0xc90.fdaa22168cp-10'), pi) |
| self.identical(fromHex('0x1921.fb54442d18p-11'), pi) |
| # ... |
| self.identical(fromHex('0x1921fb54442d1.8p-47'), pi) |
| self.identical(fromHex('0x3243f6a8885a3p-48'), pi) |
| self.identical(fromHex('0x6487ed5110b46p-49'), pi) |
| self.identical(fromHex('0xc90fdaa22168cp-50'), pi) |
| self.identical(fromHex('0x1921fb54442d18p-51'), pi) |
| self.identical(fromHex('0x3243f6a8885a30p-52'), pi) |
| self.identical(fromHex('0x6487ed5110b460p-53'), pi) |
| self.identical(fromHex('0xc90fdaa22168c0p-54'), pi) |
| self.identical(fromHex('0x1921fb54442d180p-55'), pi) |
| |
| |
| # results that should overflow... |
| self.assertRaises(OverflowError, fromHex, '-0x1p1024') |
| self.assertRaises(OverflowError, fromHex, '0x1p+1025') |
| self.assertRaises(OverflowError, fromHex, '+0X1p1030') |
| self.assertRaises(OverflowError, fromHex, '-0x1p+1100') |
| self.assertRaises(OverflowError, fromHex, '0X1p123456789123456789') |
| self.assertRaises(OverflowError, fromHex, '+0X.8p+1025') |
| self.assertRaises(OverflowError, fromHex, '+0x0.8p1025') |
| self.assertRaises(OverflowError, fromHex, '-0x0.4p1026') |
| self.assertRaises(OverflowError, fromHex, '0X2p+1023') |
| self.assertRaises(OverflowError, fromHex, '0x2.p1023') |
| self.assertRaises(OverflowError, fromHex, '-0x2.0p+1023') |
| self.assertRaises(OverflowError, fromHex, '+0X4p+1022') |
| self.assertRaises(OverflowError, fromHex, '0x1.ffffffffffffffp+1023') |
| self.assertRaises(OverflowError, fromHex, '-0X1.fffffffffffff9p1023') |
| self.assertRaises(OverflowError, fromHex, '0X1.fffffffffffff8p1023') |
| self.assertRaises(OverflowError, fromHex, '+0x3.fffffffffffffp1022') |
| self.assertRaises(OverflowError, fromHex, '0x3fffffffffffffp+970') |
| self.assertRaises(OverflowError, fromHex, '0x10000000000000000p960') |
| self.assertRaises(OverflowError, fromHex, '-0Xffffffffffffffffp960') |
| |
| # ...and those that round to +-max float |
| self.identical(fromHex('+0x1.fffffffffffffp+1023'), MAX) |
| self.identical(fromHex('-0X1.fffffffffffff7p1023'), -MAX) |
| self.identical(fromHex('0X1.fffffffffffff7fffffffffffffp1023'), MAX) |
| |
| # zeros |
| self.identical(fromHex('0x0p0'), 0.0) |
| self.identical(fromHex('0x0p1000'), 0.0) |
| self.identical(fromHex('-0x0p1023'), -0.0) |
| self.identical(fromHex('0X0p1024'), 0.0) |
| self.identical(fromHex('-0x0p1025'), -0.0) |
| self.identical(fromHex('0X0p2000'), 0.0) |
| self.identical(fromHex('0x0p123456789123456789'), 0.0) |
| self.identical(fromHex('-0X0p-0'), -0.0) |
| self.identical(fromHex('-0X0p-1000'), -0.0) |
| self.identical(fromHex('0x0p-1023'), 0.0) |
| self.identical(fromHex('-0X0p-1024'), -0.0) |
| self.identical(fromHex('-0x0p-1025'), -0.0) |
| self.identical(fromHex('-0x0p-1072'), -0.0) |
| self.identical(fromHex('0X0p-1073'), 0.0) |
| self.identical(fromHex('-0x0p-1074'), -0.0) |
| self.identical(fromHex('0x0p-1075'), 0.0) |
| self.identical(fromHex('0X0p-1076'), 0.0) |
| self.identical(fromHex('-0X0p-2000'), -0.0) |
| self.identical(fromHex('-0x0p-123456789123456789'), -0.0) |
| |
| # values that should underflow to 0 |
| self.identical(fromHex('0X1p-1075'), 0.0) |
| self.identical(fromHex('-0X1p-1075'), -0.0) |
| self.identical(fromHex('-0x1p-123456789123456789'), -0.0) |
| self.identical(fromHex('0x1.00000000000000001p-1075'), TINY) |
| self.identical(fromHex('-0x1.1p-1075'), -TINY) |
| self.identical(fromHex('0x1.fffffffffffffffffp-1075'), TINY) |
| |
| # check round-half-even is working correctly near 0 ... |
| self.identical(fromHex('0x1p-1076'), 0.0) |
| self.identical(fromHex('0X2p-1076'), 0.0) |
| self.identical(fromHex('0X3p-1076'), TINY) |
| self.identical(fromHex('0x4p-1076'), TINY) |
| self.identical(fromHex('0X5p-1076'), TINY) |
| self.identical(fromHex('0X6p-1076'), 2*TINY) |
| self.identical(fromHex('0x7p-1076'), 2*TINY) |
| self.identical(fromHex('0X8p-1076'), 2*TINY) |
| self.identical(fromHex('0X9p-1076'), 2*TINY) |
| self.identical(fromHex('0xap-1076'), 2*TINY) |
| self.identical(fromHex('0Xbp-1076'), 3*TINY) |
| self.identical(fromHex('0xcp-1076'), 3*TINY) |
| self.identical(fromHex('0Xdp-1076'), 3*TINY) |
| self.identical(fromHex('0Xep-1076'), 4*TINY) |
| self.identical(fromHex('0xfp-1076'), 4*TINY) |
| self.identical(fromHex('0x10p-1076'), 4*TINY) |
| self.identical(fromHex('-0x1p-1076'), -0.0) |
| self.identical(fromHex('-0X2p-1076'), -0.0) |
| self.identical(fromHex('-0x3p-1076'), -TINY) |
| self.identical(fromHex('-0X4p-1076'), -TINY) |
| self.identical(fromHex('-0x5p-1076'), -TINY) |
| self.identical(fromHex('-0x6p-1076'), -2*TINY) |
| self.identical(fromHex('-0X7p-1076'), -2*TINY) |
| self.identical(fromHex('-0X8p-1076'), -2*TINY) |
| self.identical(fromHex('-0X9p-1076'), -2*TINY) |
| self.identical(fromHex('-0Xap-1076'), -2*TINY) |
| self.identical(fromHex('-0xbp-1076'), -3*TINY) |
| self.identical(fromHex('-0xcp-1076'), -3*TINY) |
| self.identical(fromHex('-0Xdp-1076'), -3*TINY) |
| self.identical(fromHex('-0xep-1076'), -4*TINY) |
| self.identical(fromHex('-0Xfp-1076'), -4*TINY) |
| self.identical(fromHex('-0X10p-1076'), -4*TINY) |
| |
| # ... and near MIN ... |
| self.identical(fromHex('0x0.ffffffffffffd6p-1022'), MIN-3*TINY) |
| self.identical(fromHex('0x0.ffffffffffffd8p-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffdap-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffdcp-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffdep-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffe0p-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffe2p-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffe4p-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffe6p-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffe8p-1022'), MIN-2*TINY) |
| self.identical(fromHex('0x0.ffffffffffffeap-1022'), MIN-TINY) |
| self.identical(fromHex('0x0.ffffffffffffecp-1022'), MIN-TINY) |
| self.identical(fromHex('0x0.ffffffffffffeep-1022'), MIN-TINY) |
| self.identical(fromHex('0x0.fffffffffffff0p-1022'), MIN-TINY) |
| self.identical(fromHex('0x0.fffffffffffff2p-1022'), MIN-TINY) |
| self.identical(fromHex('0x0.fffffffffffff4p-1022'), MIN-TINY) |
| self.identical(fromHex('0x0.fffffffffffff6p-1022'), MIN-TINY) |
| self.identical(fromHex('0x0.fffffffffffff8p-1022'), MIN) |
| self.identical(fromHex('0x0.fffffffffffffap-1022'), MIN) |
| self.identical(fromHex('0x0.fffffffffffffcp-1022'), MIN) |
| self.identical(fromHex('0x0.fffffffffffffep-1022'), MIN) |
| self.identical(fromHex('0x1.00000000000000p-1022'), MIN) |
| self.identical(fromHex('0x1.00000000000002p-1022'), MIN) |
| self.identical(fromHex('0x1.00000000000004p-1022'), MIN) |
| self.identical(fromHex('0x1.00000000000006p-1022'), MIN) |
| self.identical(fromHex('0x1.00000000000008p-1022'), MIN) |
| self.identical(fromHex('0x1.0000000000000ap-1022'), MIN+TINY) |
| self.identical(fromHex('0x1.0000000000000cp-1022'), MIN+TINY) |
| self.identical(fromHex('0x1.0000000000000ep-1022'), MIN+TINY) |
| self.identical(fromHex('0x1.00000000000010p-1022'), MIN+TINY) |
| self.identical(fromHex('0x1.00000000000012p-1022'), MIN+TINY) |
| self.identical(fromHex('0x1.00000000000014p-1022'), MIN+TINY) |
| self.identical(fromHex('0x1.00000000000016p-1022'), MIN+TINY) |
| self.identical(fromHex('0x1.00000000000018p-1022'), MIN+2*TINY) |
| |
| # ... and near 1.0. |
| self.identical(fromHex('0x0.fffffffffffff0p0'), 1.0-EPS) |
| self.identical(fromHex('0x0.fffffffffffff1p0'), 1.0-EPS) |
| self.identical(fromHex('0X0.fffffffffffff2p0'), 1.0-EPS) |
| self.identical(fromHex('0x0.fffffffffffff3p0'), 1.0-EPS) |
| self.identical(fromHex('0X0.fffffffffffff4p0'), 1.0-EPS) |
| self.identical(fromHex('0X0.fffffffffffff5p0'), 1.0-EPS/2) |
| self.identical(fromHex('0X0.fffffffffffff6p0'), 1.0-EPS/2) |
| self.identical(fromHex('0x0.fffffffffffff7p0'), 1.0-EPS/2) |
| self.identical(fromHex('0x0.fffffffffffff8p0'), 1.0-EPS/2) |
| self.identical(fromHex('0X0.fffffffffffff9p0'), 1.0-EPS/2) |
| self.identical(fromHex('0X0.fffffffffffffap0'), 1.0-EPS/2) |
| self.identical(fromHex('0x0.fffffffffffffbp0'), 1.0-EPS/2) |
| self.identical(fromHex('0X0.fffffffffffffcp0'), 1.0) |
| self.identical(fromHex('0x0.fffffffffffffdp0'), 1.0) |
| self.identical(fromHex('0X0.fffffffffffffep0'), 1.0) |
| self.identical(fromHex('0x0.ffffffffffffffp0'), 1.0) |
| self.identical(fromHex('0X1.00000000000000p0'), 1.0) |
| self.identical(fromHex('0X1.00000000000001p0'), 1.0) |
| self.identical(fromHex('0x1.00000000000002p0'), 1.0) |
| self.identical(fromHex('0X1.00000000000003p0'), 1.0) |
| self.identical(fromHex('0x1.00000000000004p0'), 1.0) |
| self.identical(fromHex('0X1.00000000000005p0'), 1.0) |
| self.identical(fromHex('0X1.00000000000006p0'), 1.0) |
| self.identical(fromHex('0X1.00000000000007p0'), 1.0) |
| self.identical(fromHex('0x1.00000000000007ffffffffffffffffffffp0'), |
| 1.0) |
| self.identical(fromHex('0x1.00000000000008p0'), 1.0) |
| self.identical(fromHex('0x1.00000000000008000000000000000001p0'), |
| 1+EPS) |
| self.identical(fromHex('0X1.00000000000009p0'), 1.0+EPS) |
| self.identical(fromHex('0x1.0000000000000ap0'), 1.0+EPS) |
| self.identical(fromHex('0x1.0000000000000bp0'), 1.0+EPS) |
| self.identical(fromHex('0X1.0000000000000cp0'), 1.0+EPS) |
| self.identical(fromHex('0x1.0000000000000dp0'), 1.0+EPS) |
| self.identical(fromHex('0x1.0000000000000ep0'), 1.0+EPS) |
| self.identical(fromHex('0X1.0000000000000fp0'), 1.0+EPS) |
| self.identical(fromHex('0x1.00000000000010p0'), 1.0+EPS) |
| self.identical(fromHex('0X1.00000000000011p0'), 1.0+EPS) |
| self.identical(fromHex('0x1.00000000000012p0'), 1.0+EPS) |
| self.identical(fromHex('0X1.00000000000013p0'), 1.0+EPS) |
| self.identical(fromHex('0X1.00000000000014p0'), 1.0+EPS) |
| self.identical(fromHex('0x1.00000000000015p0'), 1.0+EPS) |
| self.identical(fromHex('0x1.00000000000016p0'), 1.0+EPS) |
| self.identical(fromHex('0X1.00000000000017p0'), 1.0+EPS) |
| self.identical(fromHex('0x1.00000000000017ffffffffffffffffffffp0'), |
| 1.0+EPS) |
| self.identical(fromHex('0x1.00000000000018p0'), 1.0+2*EPS) |
| self.identical(fromHex('0X1.00000000000018000000000000000001p0'), |
| 1.0+2*EPS) |
| self.identical(fromHex('0x1.00000000000019p0'), 1.0+2*EPS) |
| self.identical(fromHex('0X1.0000000000001ap0'), 1.0+2*EPS) |
| self.identical(fromHex('0X1.0000000000001bp0'), 1.0+2*EPS) |
| self.identical(fromHex('0x1.0000000000001cp0'), 1.0+2*EPS) |
| self.identical(fromHex('0x1.0000000000001dp0'), 1.0+2*EPS) |
| self.identical(fromHex('0x1.0000000000001ep0'), 1.0+2*EPS) |
| self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS) |
| self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS) |
| |
| def test_roundtrip(self): |
| def roundtrip(x): |
| return fromHex(toHex(x)) |
| |
| for x in [NAN, INF, self.MAX, self.MIN, self.MIN-self.TINY, self.TINY, 0.0]: |
| self.identical(x, roundtrip(x)) |
| self.identical(-x, roundtrip(-x)) |
| |
| # fromHex(toHex(x)) should exactly recover x, for any non-NaN float x. |
| import random |
| for i in range(10000): |
| e = random.randrange(-1200, 1200) |
| m = random.random() |
| s = random.choice([1.0, -1.0]) |
| try: |
| x = s*ldexp(m, e) |
| except OverflowError: |
| pass |
| else: |
| self.identical(x, fromHex(toHex(x))) |
| |
| def test_subclass(self): |
| class F(float): |
| def __new__(cls, value): |
| return float.__new__(cls, value + 1) |
| |
| f = F.fromhex((1.5).hex()) |
| self.assertIs(type(f), F) |
| self.assertEqual(f, 2.5) |
| |
| class F2(float): |
| def __init__(self, value): |
| self.foo = 'bar' |
| |
| f = F2.fromhex((1.5).hex()) |
| self.assertIs(type(f), F2) |
| self.assertEqual(f, 1.5) |
| self.assertEqual(getattr(f, 'foo', 'none'), 'bar') |
| |
| |
| if __name__ == '__main__': |
| unittest.main() |
