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import fractions import operator import os import random import sys import struct import time import unittest from test import support from test.support.testcase import FloatsAreIdenticalMixin from test.support.numbers import ( VALID_UNDERSCORE_LITERALS, INVALID_UNDERSCORE_LITERALS, ) from math import isinf, isnan, copysign, ldexp import math try: import _testcapi except ImportError: _testcapi = None INF = float("inf") NAN = float("nan") #locate file with float format test values test_dir = os.path.dirname(__file__) or os.curdir format_testfile = os.path.join(test_dir, 'mathdata', 'formatfloat_testcases.txt') class FloatSubclass(float): pass class OtherFloatSubclass(float): pass class MyIndex: def __init__(self, value): self.value = value def __index__(self): return self.value class MyInt: def __init__(self, value): self.value = value def __int__(self): return self.value class FloatLike: def __init__(self, value): self.value = value def __float__(self): return self.value 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_noargs(self): self.assertEqual(float(), 0.0) 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 ') # all whitespace (cf. https://github.com/python/cpython/issues/95605) check('') check(' ') check('\t \n') # 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 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(FloatLike(42.)), 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.) self.assertRaises(TypeError, time.sleep, FloatLike("")) # Issue #24731 f = FloatLike(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) self.assertEqual(float(MyIndex(42)), 42.0) self.assertRaises(OverflowError, float, MyIndex(2**2000)) self.assertRaises(TypeError, float, MyInt(42)) def test_keyword_args(self): with self.assertRaisesRegex(TypeError, 'keyword argument'): float(x='3.14') def test_keywords_in_subclass(self): class subclass(float): pass u = subclass(2.5) self.assertIs(type(u), subclass) self.assertEqual(float(u), 2.5) with self.assertRaises(TypeError): subclass(x=0) class subclass_with_init(float): def __init__(self, arg, newarg=None): self.newarg = newarg u = subclass_with_init(2.5, newarg=3) self.assertIs(type(u), subclass_with_init) self.assertEqual(float(u), 2.5) self.assertEqual(u.newarg, 3) class subclass_with_new(float): def __new__(cls, arg, newarg=None): self = super().__new__(cls, arg) self.newarg = newarg return self u = subclass_with_new(2.5, newarg=3) self.assertIs(type(u), subclass_with_new) self.assertEqual(float(u), 2.5) self.assertEqual(u.newarg, 3) def assertEqualAndType(self, actual, expected_value, expected_type): self.assertEqual(actual, expected_value) self.assertIs(type(actual), expected_type) def test_from_number(self, cls=float): def eq(actual, expected): self.assertEqual(actual, expected) self.assertIs(type(actual), cls) eq(cls.from_number(3.14), 3.14) eq(cls.from_number(314), 314.0) eq(cls.from_number(OtherFloatSubclass(3.14)), 3.14) eq(cls.from_number(FloatLike(3.14)), 3.14) eq(cls.from_number(MyIndex(314)), 314.0) x = cls.from_number(NAN) self.assertTrue(x != x) self.assertIs(type(x), cls) if cls is float: self.assertIs(cls.from_number(NAN), NAN) self.assertRaises(TypeError, cls.from_number, '3.14') self.assertRaises(TypeError, cls.from_number, b'3.14') self.assertRaises(TypeError, cls.from_number, 3.14j) self.assertRaises(TypeError, cls.from_number, MyInt(314)) self.assertRaises(TypeError, cls.from_number, {}) self.assertRaises(TypeError, cls.from_number) def test_from_number_subclass(self): self.test_from_number(FloatSubclass) 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))) def test_float_floor(self): self.assertIsInstance(float(0.5).__floor__(), int) self.assertEqual(float(0.5).__floor__(), 0) self.assertEqual(float(1.0).__floor__(), 1) self.assertEqual(float(1.5).__floor__(), 1) self.assertEqual(float(-0.5).__floor__(), -1) self.assertEqual(float(-1.0).__floor__(), -1) self.assertEqual(float(-1.5).__floor__(), -2) self.assertEqual(float(1.23e167).__floor__(), 1.23e167) self.assertEqual(float(-1.23e167).__floor__(), -1.23e167) self.assertRaises(ValueError, float("nan").__floor__) self.assertRaises(OverflowError, float("inf").__floor__) self.assertRaises(OverflowError, float("-inf").__floor__) def test_float_ceil(self): self.assertIsInstance(float(0.5).__ceil__(), int) self.assertEqual(float(0.5).__ceil__(), 1) self.assertEqual(float(1.0).__ceil__(), 1) self.assertEqual(float(1.5).__ceil__(), 2) self.assertEqual(float(-0.5).__ceil__(), 0) self.assertEqual(float(-1.0).__ceil__(), -1) self.assertEqual(float(-1.5).__ceil__(), -1) self.assertEqual(float(1.23e167).__ceil__(), 1.23e167) self.assertEqual(float(-1.23e167).__ceil__(), -1.23e167) self.assertRaises(ValueError, float("nan").__ceil__) self.assertRaises(OverflowError, float("inf").__ceil__) self.assertRaises(OverflowError, float("-inf").__ceil__) @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) def test_hash(self): for x in range(-30, 30): self.assertEqual(hash(float(x)), hash(x)) self.assertEqual(hash(float(sys.float_info.max)), hash(int(sys.float_info.max))) self.assertEqual(hash(float('inf')), sys.hash_info.inf) self.assertEqual(hash(float('-inf')), -sys.hash_info.inf) def test_hash_nan(self): value = float('nan') self.assertEqual(hash(value), object.__hash__(value)) class H: def __hash__(self): return 42 class F(float, H): pass value = F('nan') self.assertEqual(hash(value), object.__hash__(value)) def test_issue_gh143006(self): # When comparing negative non-integer float and int with the # same number of bits in the integer part, __neg__() in the # int subclass returning not an int caused an assertion error. class EvilInt(int): def __neg__(self): return "" i = -1 << 50 f = float(i) - 0.5 i = EvilInt(i) self.assertFalse(f == i) self.assertTrue(f != i) self.assertTrue(f < i) self.assertTrue(f <= i) self.assertFalse(f > i) self.assertFalse(f >= i) @unittest.skipUnless(hasattr(float, "__getformat__"), "requires __getformat__") class FormatFunctionsTestCase(unittest.TestCase): 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) 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 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), ('f', BE_FLOAT_INF), ('>f', BE_FLOAT_NAN), (''), 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") # confirm format options expected to fail on floats, such as integer # presentation types for format_spec in 'sbcdoxX': 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') # thousands separators x = 123_456.123_456 self.assertEqual(format(x, '_f'), '123_456.123456') self.assertEqual(format(x, ',f'), '123,456.123456') self.assertEqual(format(x, '._f'), '123456.123_456') self.assertEqual(format(x, '.,f'), '123456.123,456') self.assertEqual(format(x, '_._f'), '123_456.123_456') self.assertEqual(format(x, ',.,f'), '123,456.123,456') self.assertEqual(format(x, '.10_f'), '123456.123_456_000_0') self.assertEqual(format(x, '.10,f'), '123456.123,456,000,0') self.assertEqual(format(x, '>21._f'), ' 123456.123_456') self.assertEqual(format(x, '<21._f'), '123456.123_456 ') self.assertEqual(format(x, '+.11_e'), '+1.234_561_234_56e+05') self.assertEqual(format(x, '+.11,e'), '+1.234,561,234,56e+05') self.assertEqual(format(x, '021_._f'), '0_000_123_456.123_456') self.assertEqual(format(x, '020_._f'), '0_000_123_456.123_456') self.assertEqual(format(x, '+021_._f'), '+0_000_123_456.123_456') self.assertEqual(format(x, '21_._f'), ' 123_456.123_456') self.assertEqual(format(x, '>021_._f'), '000000123_456.123_456') self.assertEqual(format(x, '<021_._f'), '123_456.123_456000000') self.assertEqual(format(x, '023_.10_f'), '0_123_456.123_456_000_0') self.assertEqual(format(x, '022_.10_f'), '0_123_456.123_456_000_0') self.assertEqual(format(x, '+023_.10_f'), '+0_123_456.123_456_000_0') self.assertEqual(format(x, '023_.9_f'), '000_123_456.123_456_000') self.assertEqual(format(x, '021_._e'), '0_000_001.234_561e+05') self.assertEqual(format(x, '020_._e'), '0_000_001.234_561e+05') self.assertEqual(format(x, '+021_._e'), '+0_000_001.234_561e+05') self.assertEqual(format(x, '023_.10_e'), '0_001.234_561_234_6e+05') self.assertEqual(format(x, '022_.10_e'), '0_001.234_561_234_6e+05') self.assertEqual(format(x, '023_.9_e'), '000_001.234_561_235e+05') self.assertRaises(ValueError, format, x, '._6f') self.assertRaises(ValueError, format, x, '.,_f') self.assertRaises(ValueError, format, x, '.6,_f') self.assertRaises(ValueError, format, x, '.6_,f') self.assertRaises(ValueError, format, x, '.6_n') self.assertRaises(ValueError, format, x, '.6,n') @support.requires_IEEE_754 @unittest.skipUnless(sys.float_repr_style == 'short', "applies only when using short float repr style") def test_format_testfile(self): with open(format_testfile, encoding="utf-8") 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() f = float(arg) self.assertEqual(fmt % f, rhs) self.assertEqual(fmt % -f, '-' + rhs) if fmt != '%r': fmt2 = fmt[1:] self.assertEqual(format(f, fmt2), rhs) self.assertEqual(format(-f, fmt2), '-' + 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') def test_issue35560(self): self.assertEqual(format(123.0, '00'), '123.0') self.assertEqual(format(123.34, '00f'), '123.340000') self.assertEqual(format(123.34, '00e'), '1.233400e+02') self.assertEqual(format(123.34, '00g'), '123.34') self.assertEqual(format(123.34, '00.10f'), '123.3400000000') self.assertEqual(format(123.34, '00.10e'), '1.2334000000e+02') self.assertEqual(format(123.34, '00.10g'), '123.34') self.assertEqual(format(123.34, '01f'), '123.340000') self.assertEqual(format(-123.0, '00'), '-123.0') self.assertEqual(format(-123.34, '00f'), '-123.340000') self.assertEqual(format(-123.34, '00e'), '-1.233400e+02') self.assertEqual(format(-123.34, '00g'), '-123.34') self.assertEqual(format(-123.34, '00.10f'), '-123.3400000000') self.assertEqual(format(-123.34, '00.10f'), '-123.3400000000') self.assertEqual(format(-123.34, '00.10e'), '-1.2334000000e+02') self.assertEqual(format(-123.34, '00.10g'), '-123.34') class ReprTestCase(unittest.TestCase): def test_repr(self): with open(os.path.join(os.path.split(__file__)[0], 'mathdata', 'floating_points.txt'), encoding="utf-8") as floats_file: for line in floats_file: line = line.strip() if not line or line.startswith('#'): continue v = eval(line) self.assertEqual(v, eval(repr(v))) @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, FloatsAreIdenticalMixin): 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_inf_nan_ndigits(self): self.assertEqual(round(INF, 0), INF) self.assertEqual(round(-INF, 0), -INF) self.assertTrue(math.isnan(round(NAN, 0))) 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.assertFloatsAreIdentical(round(123.456, n), 0.0) self.assertFloatsAreIdentical(round(-123.456, n), -0.0) self.assertFloatsAreIdentical(round(1e300, n), 0.0) self.assertFloatsAreIdentical(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) @support.cpython_only def test_round_with_none_arg_direct_call(self): for val in [(1.0).__round__(None), round(1.0), round(1.0, None)]: self.assertEqual(val, 1) self.assertIs(type(val), 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) def test_nan_signs(self): # 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(FloatsAreIdenticalMixin, 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): self.assertFloatsAreIdentical(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) # Regression test for a corner-case bug reported in b.p.o. 44954 self.identical(fromHex('0x.8p-1074'), 0.0) self.identical(fromHex('0x.80p-1074'), 0.0) self.identical(fromHex('0x.81p-1074'), TINY) self.identical(fromHex('0x8p-1078'), 0.0) self.identical(fromHex('0x8.0p-1078'), 0.0) self.identical(fromHex('0x8.1p-1078'), TINY) self.identical(fromHex('0x80p-1082'), 0.0) self.identical(fromHex('0x81p-1082'), TINY) self.identical(fromHex('.8p-1074'), 0.0) self.identical(fromHex('8p-1078'), 0.0) self.identical(fromHex('-.8p-1074'), -0.0) self.identical(fromHex('+8p-1078'), 0.0) 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()