mirror of https://github.com/python/cpython
1648 lines
69 KiB
Python
1648 lines
69 KiB
Python
"""Tests for Lib/fractions.py."""
|
|
|
|
import cmath
|
|
from decimal import Decimal
|
|
from test.support import requires_IEEE_754
|
|
import math
|
|
import numbers
|
|
import operator
|
|
import fractions
|
|
import functools
|
|
import os
|
|
import sys
|
|
import typing
|
|
import unittest
|
|
from copy import copy, deepcopy
|
|
import pickle
|
|
from pickle import dumps, loads
|
|
F = fractions.Fraction
|
|
|
|
#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 DummyFloat(object):
|
|
"""Dummy float class for testing comparisons with Fractions"""
|
|
|
|
def __init__(self, value):
|
|
if not isinstance(value, float):
|
|
raise TypeError("DummyFloat can only be initialized from float")
|
|
self.value = value
|
|
|
|
def _richcmp(self, other, op):
|
|
if isinstance(other, numbers.Rational):
|
|
return op(F.from_float(self.value), other)
|
|
elif isinstance(other, DummyFloat):
|
|
return op(self.value, other.value)
|
|
else:
|
|
return NotImplemented
|
|
|
|
def __eq__(self, other): return self._richcmp(other, operator.eq)
|
|
def __le__(self, other): return self._richcmp(other, operator.le)
|
|
def __lt__(self, other): return self._richcmp(other, operator.lt)
|
|
def __ge__(self, other): return self._richcmp(other, operator.ge)
|
|
def __gt__(self, other): return self._richcmp(other, operator.gt)
|
|
|
|
# shouldn't be calling __float__ at all when doing comparisons
|
|
def __float__(self):
|
|
assert False, "__float__ should not be invoked for comparisons"
|
|
|
|
# same goes for subtraction
|
|
def __sub__(self, other):
|
|
assert False, "__sub__ should not be invoked for comparisons"
|
|
__rsub__ = __sub__
|
|
|
|
|
|
class DummyRational(object):
|
|
"""Test comparison of Fraction with a naive rational implementation."""
|
|
|
|
def __init__(self, num, den):
|
|
g = math.gcd(num, den)
|
|
self.num = num // g
|
|
self.den = den // g
|
|
|
|
def __eq__(self, other):
|
|
if isinstance(other, fractions.Fraction):
|
|
return (self.num == other._numerator and
|
|
self.den == other._denominator)
|
|
else:
|
|
return NotImplemented
|
|
|
|
def __lt__(self, other):
|
|
return(self.num * other._denominator < self.den * other._numerator)
|
|
|
|
def __gt__(self, other):
|
|
return(self.num * other._denominator > self.den * other._numerator)
|
|
|
|
def __le__(self, other):
|
|
return(self.num * other._denominator <= self.den * other._numerator)
|
|
|
|
def __ge__(self, other):
|
|
return(self.num * other._denominator >= self.den * other._numerator)
|
|
|
|
# this class is for testing comparisons; conversion to float
|
|
# should never be used for a comparison, since it loses accuracy
|
|
def __float__(self):
|
|
assert False, "__float__ should not be invoked"
|
|
|
|
class DummyFraction(fractions.Fraction):
|
|
"""Dummy Fraction subclass for copy and deepcopy testing."""
|
|
|
|
|
|
def _components(r):
|
|
return (r.numerator, r.denominator)
|
|
|
|
def typed_approx_eq(a, b):
|
|
return type(a) == type(b) and (a == b or math.isclose(a, b))
|
|
|
|
class Symbolic:
|
|
"""Simple non-numeric class for testing mixed arithmetic.
|
|
It is not Integral, Rational, Real or Complex, and cannot be conveted
|
|
to int, float or complex. but it supports some arithmetic operations.
|
|
"""
|
|
def __init__(self, value):
|
|
self.value = value
|
|
def __mul__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(f'{self} * {other}')
|
|
def __rmul__(self, other):
|
|
return self.__class__(f'{other} * {self}')
|
|
def __truediv__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(f'{self} / {other}')
|
|
def __rtruediv__(self, other):
|
|
return self.__class__(f'{other} / {self}')
|
|
def __mod__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(f'{self} % {other}')
|
|
def __rmod__(self, other):
|
|
return self.__class__(f'{other} % {self}')
|
|
def __pow__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(f'{self} ** {other}')
|
|
def __rpow__(self, other):
|
|
return self.__class__(f'{other} ** {self}')
|
|
def __eq__(self, other):
|
|
if other.__class__ != self.__class__:
|
|
return NotImplemented
|
|
return self.value == other.value
|
|
def __str__(self):
|
|
return f'{self.value}'
|
|
def __repr__(self):
|
|
return f'{self.__class__.__name__}({self.value!r})'
|
|
|
|
class SymbolicReal(Symbolic):
|
|
pass
|
|
numbers.Real.register(SymbolicReal)
|
|
|
|
class SymbolicComplex(Symbolic):
|
|
pass
|
|
numbers.Complex.register(SymbolicComplex)
|
|
|
|
class Rat:
|
|
"""Simple Rational class for testing mixed arithmetic."""
|
|
def __init__(self, n, d):
|
|
self.numerator = n
|
|
self.denominator = d
|
|
def __mul__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.numerator * other.numerator,
|
|
self.denominator * other.denominator)
|
|
def __rmul__(self, other):
|
|
return self.__class__(other.numerator * self.numerator,
|
|
other.denominator * self.denominator)
|
|
def __truediv__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.numerator * other.denominator,
|
|
self.denominator * other.numerator)
|
|
def __rtruediv__(self, other):
|
|
return self.__class__(other.numerator * self.denominator,
|
|
other.denominator * self.numerator)
|
|
def __mod__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
d = self.denominator * other.numerator
|
|
return self.__class__(self.numerator * other.denominator % d, d)
|
|
def __rmod__(self, other):
|
|
d = other.denominator * self.numerator
|
|
return self.__class__(other.numerator * self.denominator % d, d)
|
|
|
|
return self.__class__(other.numerator / self.numerator,
|
|
other.denominator / self.denominator)
|
|
def __pow__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.numerator ** other,
|
|
self.denominator ** other)
|
|
def __float__(self):
|
|
return self.numerator / self.denominator
|
|
def __eq__(self, other):
|
|
if self.__class__ != other.__class__:
|
|
return NotImplemented
|
|
return (typed_approx_eq(self.numerator, other.numerator) and
|
|
typed_approx_eq(self.denominator, other.denominator))
|
|
def __repr__(self):
|
|
return f'{self.__class__.__name__}({self.numerator!r}, {self.denominator!r})'
|
|
numbers.Rational.register(Rat)
|
|
|
|
class Root:
|
|
"""Simple Real class for testing mixed arithmetic."""
|
|
def __init__(self, v, n=F(2)):
|
|
self.base = v
|
|
self.degree = n
|
|
def __mul__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.base * other**self.degree, self.degree)
|
|
def __rmul__(self, other):
|
|
return self.__class__(other**self.degree * self.base, self.degree)
|
|
def __truediv__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.base / other**self.degree, self.degree)
|
|
def __rtruediv__(self, other):
|
|
return self.__class__(other**self.degree / self.base, self.degree)
|
|
def __pow__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.base, self.degree / other)
|
|
def __float__(self):
|
|
return float(self.base) ** (1 / float(self.degree))
|
|
def __eq__(self, other):
|
|
if self.__class__ != other.__class__:
|
|
return NotImplemented
|
|
return typed_approx_eq(self.base, other.base) and typed_approx_eq(self.degree, other.degree)
|
|
def __repr__(self):
|
|
return f'{self.__class__.__name__}({self.base!r}, {self.degree!r})'
|
|
numbers.Real.register(Root)
|
|
|
|
class Polar:
|
|
"""Simple Complex class for testing mixed arithmetic."""
|
|
def __init__(self, r, phi):
|
|
self.r = r
|
|
self.phi = phi
|
|
def __mul__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.r * other, self.phi)
|
|
def __rmul__(self, other):
|
|
return self.__class__(other * self.r, self.phi)
|
|
def __truediv__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.r / other, self.phi)
|
|
def __rtruediv__(self, other):
|
|
return self.__class__(other / self.r, -self.phi)
|
|
def __pow__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.r ** other, self.phi * other)
|
|
def __eq__(self, other):
|
|
if self.__class__ != other.__class__:
|
|
return NotImplemented
|
|
return typed_approx_eq(self.r, other.r) and typed_approx_eq(self.phi, other.phi)
|
|
def __repr__(self):
|
|
return f'{self.__class__.__name__}({self.r!r}, {self.phi!r})'
|
|
numbers.Complex.register(Polar)
|
|
|
|
class Rect:
|
|
"""Other simple Complex class for testing mixed arithmetic."""
|
|
def __init__(self, x, y):
|
|
self.x = x
|
|
self.y = y
|
|
def __mul__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.x * other, self.y * other)
|
|
def __rmul__(self, other):
|
|
return self.__class__(other * self.x, other * self.y)
|
|
def __truediv__(self, other):
|
|
if isinstance(other, F):
|
|
return NotImplemented
|
|
return self.__class__(self.x / other, self.y / other)
|
|
def __rtruediv__(self, other):
|
|
r = self.x * self.x + self.y * self.y
|
|
return self.__class__(other * (self.x / r), other * (self.y / r))
|
|
def __rpow__(self, other):
|
|
return Polar(other ** self.x, math.log(other) * self.y)
|
|
def __complex__(self):
|
|
return complex(self.x, self.y)
|
|
def __eq__(self, other):
|
|
if self.__class__ != other.__class__:
|
|
return NotImplemented
|
|
return typed_approx_eq(self.x, other.x) and typed_approx_eq(self.y, other.y)
|
|
def __repr__(self):
|
|
return f'{self.__class__.__name__}({self.x!r}, {self.y!r})'
|
|
numbers.Complex.register(Rect)
|
|
|
|
class RectComplex(Rect, complex):
|
|
pass
|
|
|
|
class FractionTest(unittest.TestCase):
|
|
|
|
def assertTypedEquals(self, expected, actual):
|
|
"""Asserts that both the types and values are the same."""
|
|
self.assertEqual(type(expected), type(actual))
|
|
self.assertEqual(expected, actual)
|
|
|
|
def assertTypedTupleEquals(self, expected, actual):
|
|
"""Asserts that both the types and values in the tuples are the same."""
|
|
self.assertTupleEqual(expected, actual)
|
|
self.assertListEqual(list(map(type, expected)), list(map(type, actual)))
|
|
|
|
def assertRaisesMessage(self, exc_type, message,
|
|
callable, *args, **kwargs):
|
|
"""Asserts that callable(*args, **kwargs) raises exc_type(message)."""
|
|
try:
|
|
callable(*args, **kwargs)
|
|
except exc_type as e:
|
|
self.assertEqual(message, str(e))
|
|
else:
|
|
self.fail("%s not raised" % exc_type.__name__)
|
|
|
|
def testInit(self):
|
|
self.assertEqual((0, 1), _components(F()))
|
|
self.assertEqual((7, 1), _components(F(7)))
|
|
self.assertEqual((7, 3), _components(F(F(7, 3))))
|
|
|
|
self.assertEqual((-1, 1), _components(F(-1, 1)))
|
|
self.assertEqual((-1, 1), _components(F(1, -1)))
|
|
self.assertEqual((1, 1), _components(F(-2, -2)))
|
|
self.assertEqual((1, 2), _components(F(5, 10)))
|
|
self.assertEqual((7, 15), _components(F(7, 15)))
|
|
self.assertEqual((10**23, 1), _components(F(10**23)))
|
|
|
|
self.assertEqual((3, 77), _components(F(F(3, 7), 11)))
|
|
self.assertEqual((-9, 5), _components(F(2, F(-10, 9))))
|
|
self.assertEqual((2486, 2485), _components(F(F(22, 7), F(355, 113))))
|
|
|
|
self.assertRaisesMessage(ZeroDivisionError, "Fraction(12, 0)",
|
|
F, 12, 0)
|
|
self.assertRaises(TypeError, F, 1.5 + 3j)
|
|
|
|
self.assertRaises(TypeError, F, "3/2", 3)
|
|
self.assertRaises(TypeError, F, 3, 0j)
|
|
self.assertRaises(TypeError, F, 3, 1j)
|
|
self.assertRaises(TypeError, F, 1, 2, 3)
|
|
|
|
@requires_IEEE_754
|
|
def testInitFromFloat(self):
|
|
self.assertEqual((5, 2), _components(F(2.5)))
|
|
self.assertEqual((0, 1), _components(F(-0.0)))
|
|
self.assertEqual((3602879701896397, 36028797018963968),
|
|
_components(F(0.1)))
|
|
# bug 16469: error types should be consistent with float -> int
|
|
self.assertRaises(ValueError, F, float('nan'))
|
|
self.assertRaises(OverflowError, F, float('inf'))
|
|
self.assertRaises(OverflowError, F, float('-inf'))
|
|
|
|
def testInitFromDecimal(self):
|
|
self.assertEqual((11, 10),
|
|
_components(F(Decimal('1.1'))))
|
|
self.assertEqual((7, 200),
|
|
_components(F(Decimal('3.5e-2'))))
|
|
self.assertEqual((0, 1),
|
|
_components(F(Decimal('.000e20'))))
|
|
# bug 16469: error types should be consistent with decimal -> int
|
|
self.assertRaises(ValueError, F, Decimal('nan'))
|
|
self.assertRaises(ValueError, F, Decimal('snan'))
|
|
self.assertRaises(OverflowError, F, Decimal('inf'))
|
|
self.assertRaises(OverflowError, F, Decimal('-inf'))
|
|
|
|
def testFromString(self):
|
|
self.assertEqual((5, 1), _components(F("5")))
|
|
self.assertEqual((3, 2), _components(F("3/2")))
|
|
self.assertEqual((3, 2), _components(F("3 / 2")))
|
|
self.assertEqual((3, 2), _components(F(" \n +3/2")))
|
|
self.assertEqual((-3, 2), _components(F("-3/2 ")))
|
|
self.assertEqual((13, 2), _components(F(" 013/02 \n ")))
|
|
self.assertEqual((16, 5), _components(F(" 3.2 ")))
|
|
self.assertEqual((-16, 5), _components(F(" -3.2 ")))
|
|
self.assertEqual((-3, 1), _components(F(" -3. ")))
|
|
self.assertEqual((3, 5), _components(F(" .6 ")))
|
|
self.assertEqual((1, 3125), _components(F("32.e-5")))
|
|
self.assertEqual((1000000, 1), _components(F("1E+06")))
|
|
self.assertEqual((-12300, 1), _components(F("-1.23e4")))
|
|
self.assertEqual((0, 1), _components(F(" .0e+0\t")))
|
|
self.assertEqual((0, 1), _components(F("-0.000e0")))
|
|
self.assertEqual((123, 1), _components(F("1_2_3")))
|
|
self.assertEqual((41, 107), _components(F("1_2_3/3_2_1")))
|
|
self.assertEqual((6283, 2000), _components(F("3.14_15")))
|
|
self.assertEqual((6283, 2*10**13), _components(F("3.14_15e-1_0")))
|
|
self.assertEqual((101, 100), _components(F("1.01")))
|
|
self.assertEqual((101, 100), _components(F("1.0_1")))
|
|
|
|
self.assertRaisesMessage(
|
|
ZeroDivisionError, "Fraction(3, 0)",
|
|
F, "3/0")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '3/'",
|
|
F, "3/")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '/2'",
|
|
F, "/2")
|
|
self.assertRaisesMessage(
|
|
# Denominators don't need a sign.
|
|
ValueError, "Invalid literal for Fraction: '3/+2'",
|
|
F, "3/+2")
|
|
self.assertRaisesMessage(
|
|
# Imitate float's parsing.
|
|
ValueError, "Invalid literal for Fraction: '+ 3/2'",
|
|
F, "+ 3/2")
|
|
self.assertRaisesMessage(
|
|
# Avoid treating '.' as a regex special character.
|
|
ValueError, "Invalid literal for Fraction: '3a2'",
|
|
F, "3a2")
|
|
self.assertRaisesMessage(
|
|
# Don't accept combinations of decimals and rationals.
|
|
ValueError, "Invalid literal for Fraction: '3/7.2'",
|
|
F, "3/7.2")
|
|
self.assertRaisesMessage(
|
|
# Don't accept combinations of decimals and rationals.
|
|
ValueError, "Invalid literal for Fraction: '3.2/7'",
|
|
F, "3.2/7")
|
|
self.assertRaisesMessage(
|
|
# Allow 3. and .3, but not .
|
|
ValueError, "Invalid literal for Fraction: '.'",
|
|
F, ".")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '_'",
|
|
F, "_")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '_1'",
|
|
F, "_1")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1__2'",
|
|
F, "1__2")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '/_'",
|
|
F, "/_")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1_/'",
|
|
F, "1_/")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '_1/'",
|
|
F, "_1/")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1__2/'",
|
|
F, "1__2/")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1/_'",
|
|
F, "1/_")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1/_1'",
|
|
F, "1/_1")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1/1__2'",
|
|
F, "1/1__2")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1._111'",
|
|
F, "1._111")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1.1__1'",
|
|
F, "1.1__1")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1.1e+_1'",
|
|
F, "1.1e+_1")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1.1e+1__1'",
|
|
F, "1.1e+1__1")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '123.dd'",
|
|
F, "123.dd")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '123.5_dd'",
|
|
F, "123.5_dd")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: 'dd.5'",
|
|
F, "dd.5")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '7_dd'",
|
|
F, "7_dd")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1/dd'",
|
|
F, "1/dd")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1/123_dd'",
|
|
F, "1/123_dd")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '789edd'",
|
|
F, "789edd")
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '789e2_dd'",
|
|
F, "789e2_dd")
|
|
# Test catastrophic backtracking.
|
|
val = "9"*50 + "_"
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '" + val + "'",
|
|
F, val)
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1/" + val + "'",
|
|
F, "1/" + val)
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1." + val + "'",
|
|
F, "1." + val)
|
|
self.assertRaisesMessage(
|
|
ValueError, "Invalid literal for Fraction: '1.1+e" + val + "'",
|
|
F, "1.1+e" + val)
|
|
|
|
def testImmutable(self):
|
|
r = F(7, 3)
|
|
r.__init__(2, 15)
|
|
self.assertEqual((7, 3), _components(r))
|
|
|
|
self.assertRaises(AttributeError, setattr, r, 'numerator', 12)
|
|
self.assertRaises(AttributeError, setattr, r, 'denominator', 6)
|
|
self.assertEqual((7, 3), _components(r))
|
|
|
|
# But if you _really_ need to:
|
|
r._numerator = 4
|
|
r._denominator = 2
|
|
self.assertEqual((4, 2), _components(r))
|
|
# Which breaks some important operations:
|
|
self.assertNotEqual(F(4, 2), r)
|
|
|
|
def testFromFloat(self):
|
|
self.assertRaises(TypeError, F.from_float, 3+4j)
|
|
self.assertEqual((10, 1), _components(F.from_float(10)))
|
|
bigint = 1234567890123456789
|
|
self.assertEqual((bigint, 1), _components(F.from_float(bigint)))
|
|
self.assertEqual((0, 1), _components(F.from_float(-0.0)))
|
|
self.assertEqual((10, 1), _components(F.from_float(10.0)))
|
|
self.assertEqual((-5, 2), _components(F.from_float(-2.5)))
|
|
self.assertEqual((99999999999999991611392, 1),
|
|
_components(F.from_float(1e23)))
|
|
self.assertEqual(float(10**23), float(F.from_float(1e23)))
|
|
self.assertEqual((3602879701896397, 1125899906842624),
|
|
_components(F.from_float(3.2)))
|
|
self.assertEqual(3.2, float(F.from_float(3.2)))
|
|
|
|
inf = 1e1000
|
|
nan = inf - inf
|
|
# bug 16469: error types should be consistent with float -> int
|
|
self.assertRaisesMessage(
|
|
OverflowError, "cannot convert Infinity to integer ratio",
|
|
F.from_float, inf)
|
|
self.assertRaisesMessage(
|
|
OverflowError, "cannot convert Infinity to integer ratio",
|
|
F.from_float, -inf)
|
|
self.assertRaisesMessage(
|
|
ValueError, "cannot convert NaN to integer ratio",
|
|
F.from_float, nan)
|
|
|
|
def testFromDecimal(self):
|
|
self.assertRaises(TypeError, F.from_decimal, 3+4j)
|
|
self.assertEqual(F(10, 1), F.from_decimal(10))
|
|
self.assertEqual(F(0), F.from_decimal(Decimal("-0")))
|
|
self.assertEqual(F(5, 10), F.from_decimal(Decimal("0.5")))
|
|
self.assertEqual(F(5, 1000), F.from_decimal(Decimal("5e-3")))
|
|
self.assertEqual(F(5000), F.from_decimal(Decimal("5e3")))
|
|
self.assertEqual(1 - F(1, 10**30),
|
|
F.from_decimal(Decimal("0." + "9" * 30)))
|
|
|
|
# bug 16469: error types should be consistent with decimal -> int
|
|
self.assertRaisesMessage(
|
|
OverflowError, "cannot convert Infinity to integer ratio",
|
|
F.from_decimal, Decimal("inf"))
|
|
self.assertRaisesMessage(
|
|
OverflowError, "cannot convert Infinity to integer ratio",
|
|
F.from_decimal, Decimal("-inf"))
|
|
self.assertRaisesMessage(
|
|
ValueError, "cannot convert NaN to integer ratio",
|
|
F.from_decimal, Decimal("nan"))
|
|
self.assertRaisesMessage(
|
|
ValueError, "cannot convert NaN to integer ratio",
|
|
F.from_decimal, Decimal("snan"))
|
|
|
|
def test_is_integer(self):
|
|
self.assertTrue(F(1, 1).is_integer())
|
|
self.assertTrue(F(-1, 1).is_integer())
|
|
self.assertTrue(F(1, -1).is_integer())
|
|
self.assertTrue(F(2, 2).is_integer())
|
|
self.assertTrue(F(-2, 2).is_integer())
|
|
self.assertTrue(F(2, -2).is_integer())
|
|
|
|
self.assertFalse(F(1, 2).is_integer())
|
|
self.assertFalse(F(-1, 2).is_integer())
|
|
self.assertFalse(F(1, -2).is_integer())
|
|
self.assertFalse(F(-1, -2).is_integer())
|
|
|
|
def test_as_integer_ratio(self):
|
|
self.assertEqual(F(4, 6).as_integer_ratio(), (2, 3))
|
|
self.assertEqual(F(-4, 6).as_integer_ratio(), (-2, 3))
|
|
self.assertEqual(F(4, -6).as_integer_ratio(), (-2, 3))
|
|
self.assertEqual(F(0, 6).as_integer_ratio(), (0, 1))
|
|
|
|
def testLimitDenominator(self):
|
|
rpi = F('3.1415926535897932')
|
|
self.assertEqual(rpi.limit_denominator(10000), F(355, 113))
|
|
self.assertEqual(-rpi.limit_denominator(10000), F(-355, 113))
|
|
self.assertEqual(rpi.limit_denominator(113), F(355, 113))
|
|
self.assertEqual(rpi.limit_denominator(112), F(333, 106))
|
|
self.assertEqual(F(201, 200).limit_denominator(100), F(1))
|
|
self.assertEqual(F(201, 200).limit_denominator(101), F(102, 101))
|
|
self.assertEqual(F(0).limit_denominator(10000), F(0))
|
|
for i in (0, -1):
|
|
self.assertRaisesMessage(
|
|
ValueError, "max_denominator should be at least 1",
|
|
F(1).limit_denominator, i)
|
|
|
|
def testConversions(self):
|
|
self.assertTypedEquals(-1, math.trunc(F(-11, 10)))
|
|
self.assertTypedEquals(1, math.trunc(F(11, 10)))
|
|
self.assertTypedEquals(-2, math.floor(F(-11, 10)))
|
|
self.assertTypedEquals(-1, math.ceil(F(-11, 10)))
|
|
self.assertTypedEquals(-1, math.ceil(F(-10, 10)))
|
|
self.assertTypedEquals(-1, int(F(-11, 10)))
|
|
self.assertTypedEquals(0, round(F(-1, 10)))
|
|
self.assertTypedEquals(0, round(F(-5, 10)))
|
|
self.assertTypedEquals(-2, round(F(-15, 10)))
|
|
self.assertTypedEquals(-1, round(F(-7, 10)))
|
|
|
|
self.assertEqual(False, bool(F(0, 1)))
|
|
self.assertEqual(True, bool(F(3, 2)))
|
|
self.assertTypedEquals(0.1, float(F(1, 10)))
|
|
|
|
# Check that __float__ isn't implemented by converting the
|
|
# numerator and denominator to float before dividing.
|
|
self.assertRaises(OverflowError, float, int('2'*400+'7'))
|
|
self.assertAlmostEqual(2.0/3,
|
|
float(F(int('2'*400+'7'), int('3'*400+'1'))))
|
|
|
|
self.assertTypedEquals(0.1+0j, complex(F(1,10)))
|
|
|
|
def testSupportsInt(self):
|
|
# See bpo-44547.
|
|
f = F(3, 2)
|
|
self.assertIsInstance(f, typing.SupportsInt)
|
|
self.assertEqual(int(f), 1)
|
|
self.assertEqual(type(int(f)), int)
|
|
|
|
def testIntGuaranteesIntReturn(self):
|
|
# Check that int(some_fraction) gives a result of exact type `int`
|
|
# even if the fraction is using some other Integral type for its
|
|
# numerator and denominator.
|
|
|
|
class CustomInt(int):
|
|
"""
|
|
Subclass of int with just enough machinery to convince the Fraction
|
|
constructor to produce something with CustomInt numerator and
|
|
denominator.
|
|
"""
|
|
|
|
@property
|
|
def numerator(self):
|
|
return self
|
|
|
|
@property
|
|
def denominator(self):
|
|
return CustomInt(1)
|
|
|
|
def __mul__(self, other):
|
|
return CustomInt(int(self) * int(other))
|
|
|
|
def __floordiv__(self, other):
|
|
return CustomInt(int(self) // int(other))
|
|
|
|
f = F(CustomInt(13), CustomInt(5))
|
|
|
|
self.assertIsInstance(f.numerator, CustomInt)
|
|
self.assertIsInstance(f.denominator, CustomInt)
|
|
self.assertIsInstance(f, typing.SupportsInt)
|
|
self.assertEqual(int(f), 2)
|
|
self.assertEqual(type(int(f)), int)
|
|
|
|
def testBoolGuarateesBoolReturn(self):
|
|
# Ensure that __bool__ is used on numerator which guarantees a bool
|
|
# return. See also bpo-39274.
|
|
@functools.total_ordering
|
|
class CustomValue:
|
|
denominator = 1
|
|
|
|
def __init__(self, value):
|
|
self.value = value
|
|
|
|
def __bool__(self):
|
|
return bool(self.value)
|
|
|
|
@property
|
|
def numerator(self):
|
|
# required to preserve `self` during instantiation
|
|
return self
|
|
|
|
def __eq__(self, other):
|
|
raise AssertionError("Avoid comparisons in Fraction.__bool__")
|
|
|
|
__lt__ = __eq__
|
|
|
|
# We did not implement all abstract methods, so register:
|
|
numbers.Rational.register(CustomValue)
|
|
|
|
numerator = CustomValue(1)
|
|
r = F(numerator)
|
|
# ensure the numerator was not lost during instantiation:
|
|
self.assertIs(r.numerator, numerator)
|
|
self.assertIs(bool(r), True)
|
|
|
|
numerator = CustomValue(0)
|
|
r = F(numerator)
|
|
self.assertIs(bool(r), False)
|
|
|
|
def testRound(self):
|
|
self.assertTypedEquals(F(-200), round(F(-150), -2))
|
|
self.assertTypedEquals(F(-200), round(F(-250), -2))
|
|
self.assertTypedEquals(F(30), round(F(26), -1))
|
|
self.assertTypedEquals(F(-2, 10), round(F(-15, 100), 1))
|
|
self.assertTypedEquals(F(-2, 10), round(F(-25, 100), 1))
|
|
|
|
def testArithmetic(self):
|
|
self.assertEqual(F(1, 2), F(1, 10) + F(2, 5))
|
|
self.assertEqual(F(-3, 10), F(1, 10) - F(2, 5))
|
|
self.assertEqual(F(1, 25), F(1, 10) * F(2, 5))
|
|
self.assertEqual(F(5, 6), F(2, 3) * F(5, 4))
|
|
self.assertEqual(F(1, 4), F(1, 10) / F(2, 5))
|
|
self.assertEqual(F(-15, 8), F(3, 4) / F(-2, 5))
|
|
self.assertRaises(ZeroDivisionError, operator.truediv, F(1), F(0))
|
|
self.assertTypedEquals(2, F(9, 10) // F(2, 5))
|
|
self.assertTypedEquals(10**23, F(10**23, 1) // F(1))
|
|
self.assertEqual(F(5, 6), F(7, 3) % F(3, 2))
|
|
self.assertEqual(F(2, 3), F(-7, 3) % F(3, 2))
|
|
self.assertEqual((F(1), F(5, 6)), divmod(F(7, 3), F(3, 2)))
|
|
self.assertEqual((F(-2), F(2, 3)), divmod(F(-7, 3), F(3, 2)))
|
|
self.assertEqual(F(8, 27), F(2, 3) ** F(3))
|
|
self.assertEqual(F(27, 8), F(2, 3) ** F(-3))
|
|
self.assertTypedEquals(2.0, F(4) ** F(1, 2))
|
|
self.assertEqual(F(1, 1), +F(1, 1))
|
|
z = pow(F(-1), F(1, 2))
|
|
self.assertAlmostEqual(z.real, 0)
|
|
self.assertEqual(z.imag, 1)
|
|
# Regression test for #27539.
|
|
p = F(-1, 2) ** 0
|
|
self.assertEqual(p, F(1, 1))
|
|
self.assertEqual(p.numerator, 1)
|
|
self.assertEqual(p.denominator, 1)
|
|
p = F(-1, 2) ** -1
|
|
self.assertEqual(p, F(-2, 1))
|
|
self.assertEqual(p.numerator, -2)
|
|
self.assertEqual(p.denominator, 1)
|
|
p = F(-1, 2) ** -2
|
|
self.assertEqual(p, F(4, 1))
|
|
self.assertEqual(p.numerator, 4)
|
|
self.assertEqual(p.denominator, 1)
|
|
|
|
def testLargeArithmetic(self):
|
|
self.assertTypedEquals(
|
|
F(10101010100808080808080808101010101010000000000000000,
|
|
1010101010101010101010101011111111101010101010101010101010101),
|
|
F(10**35+1, 10**27+1) % F(10**27+1, 10**35-1)
|
|
)
|
|
self.assertTypedEquals(
|
|
F(7, 1901475900342344102245054808064),
|
|
F(-2**100, 3) % F(5, 2**100)
|
|
)
|
|
self.assertTypedTupleEquals(
|
|
(9999999999999999,
|
|
F(10101010100808080808080808101010101010000000000000000,
|
|
1010101010101010101010101011111111101010101010101010101010101)),
|
|
divmod(F(10**35+1, 10**27+1), F(10**27+1, 10**35-1))
|
|
)
|
|
self.assertTypedEquals(
|
|
-2 ** 200 // 15,
|
|
F(-2**100, 3) // F(5, 2**100)
|
|
)
|
|
self.assertTypedEquals(
|
|
1,
|
|
F(5, 2**100) // F(3, 2**100)
|
|
)
|
|
self.assertTypedEquals(
|
|
(1, F(2, 2**100)),
|
|
divmod(F(5, 2**100), F(3, 2**100))
|
|
)
|
|
self.assertTypedTupleEquals(
|
|
(-2 ** 200 // 15,
|
|
F(7, 1901475900342344102245054808064)),
|
|
divmod(F(-2**100, 3), F(5, 2**100))
|
|
)
|
|
|
|
def testMixedArithmetic(self):
|
|
self.assertTypedEquals(F(11, 10), F(1, 10) + 1)
|
|
self.assertTypedEquals(1.1, F(1, 10) + 1.0)
|
|
self.assertTypedEquals(1.1 + 0j, F(1, 10) + (1.0 + 0j))
|
|
self.assertTypedEquals(F(11, 10), 1 + F(1, 10))
|
|
self.assertTypedEquals(1.1, 1.0 + F(1, 10))
|
|
self.assertTypedEquals(1.1 + 0j, (1.0 + 0j) + F(1, 10))
|
|
|
|
self.assertTypedEquals(F(-9, 10), F(1, 10) - 1)
|
|
self.assertTypedEquals(-0.9, F(1, 10) - 1.0)
|
|
self.assertTypedEquals(-0.9 + 0j, F(1, 10) - (1.0 + 0j))
|
|
self.assertTypedEquals(F(9, 10), 1 - F(1, 10))
|
|
self.assertTypedEquals(0.9, 1.0 - F(1, 10))
|
|
self.assertTypedEquals(0.9 + 0j, (1.0 + 0j) - F(1, 10))
|
|
|
|
def testMixedMultiplication(self):
|
|
self.assertTypedEquals(F(1, 10), F(1, 10) * 1)
|
|
self.assertTypedEquals(0.1, F(1, 10) * 1.0)
|
|
self.assertTypedEquals(0.1 + 0j, F(1, 10) * (1.0 + 0j))
|
|
self.assertTypedEquals(F(1, 10), 1 * F(1, 10))
|
|
self.assertTypedEquals(0.1, 1.0 * F(1, 10))
|
|
self.assertTypedEquals(0.1 + 0j, (1.0 + 0j) * F(1, 10))
|
|
|
|
self.assertTypedEquals(F(3, 2) * DummyFraction(5, 3), F(5, 2))
|
|
self.assertTypedEquals(DummyFraction(5, 3) * F(3, 2), F(5, 2))
|
|
self.assertTypedEquals(F(3, 2) * Rat(5, 3), Rat(15, 6))
|
|
self.assertTypedEquals(Rat(5, 3) * F(3, 2), F(5, 2))
|
|
|
|
self.assertTypedEquals(F(3, 2) * Root(4), Root(F(9, 1)))
|
|
self.assertTypedEquals(Root(4) * F(3, 2), 3.0)
|
|
self.assertEqual(F(3, 2) * SymbolicReal('X'), SymbolicReal('3/2 * X'))
|
|
self.assertRaises(TypeError, operator.mul, SymbolicReal('X'), F(3, 2))
|
|
|
|
self.assertTypedEquals(F(3, 2) * Polar(4, 2), Polar(F(6, 1), 2))
|
|
self.assertTypedEquals(F(3, 2) * Polar(4.0, 2), Polar(6.0, 2))
|
|
self.assertTypedEquals(F(3, 2) * Rect(4, 3), Rect(F(6, 1), F(9, 2)))
|
|
with self.assertWarnsRegex(DeprecationWarning,
|
|
"argument 'real' must be a real number, not complex"):
|
|
self.assertTypedEquals(F(3, 2) * RectComplex(4, 3),
|
|
RectComplex(6.0+0j, 4.5+0j))
|
|
self.assertRaises(TypeError, operator.mul, Polar(4, 2), F(3, 2))
|
|
self.assertTypedEquals(Rect(4, 3) * F(3, 2), 6.0 + 4.5j)
|
|
self.assertEqual(F(3, 2) * SymbolicComplex('X'), SymbolicComplex('3/2 * X'))
|
|
self.assertRaises(TypeError, operator.mul, SymbolicComplex('X'), F(3, 2))
|
|
|
|
self.assertEqual(F(3, 2) * Symbolic('X'), Symbolic('3/2 * X'))
|
|
self.assertRaises(TypeError, operator.mul, Symbolic('X'), F(3, 2))
|
|
|
|
def testMixedDivision(self):
|
|
self.assertTypedEquals(F(1, 10), F(1, 10) / 1)
|
|
self.assertTypedEquals(0.1, F(1, 10) / 1.0)
|
|
self.assertTypedEquals(0.1 + 0j, F(1, 10) / (1.0 + 0j))
|
|
self.assertTypedEquals(F(10, 1), 1 / F(1, 10))
|
|
self.assertTypedEquals(10.0, 1.0 / F(1, 10))
|
|
self.assertTypedEquals(10.0 + 0j, (1.0 + 0j) / F(1, 10))
|
|
|
|
self.assertTypedEquals(F(3, 2) / DummyFraction(3, 5), F(5, 2))
|
|
self.assertTypedEquals(DummyFraction(5, 3) / F(2, 3), F(5, 2))
|
|
self.assertTypedEquals(F(3, 2) / Rat(3, 5), Rat(15, 6))
|
|
self.assertTypedEquals(Rat(5, 3) / F(2, 3), F(5, 2))
|
|
|
|
self.assertTypedEquals(F(2, 3) / Root(4), Root(F(1, 9)))
|
|
self.assertTypedEquals(Root(4) / F(2, 3), 3.0)
|
|
self.assertEqual(F(3, 2) / SymbolicReal('X'), SymbolicReal('3/2 / X'))
|
|
self.assertRaises(TypeError, operator.truediv, SymbolicReal('X'), F(3, 2))
|
|
|
|
self.assertTypedEquals(F(3, 2) / Polar(4, 2), Polar(F(3, 8), -2))
|
|
self.assertTypedEquals(F(3, 2) / Polar(4.0, 2), Polar(0.375, -2))
|
|
self.assertTypedEquals(F(3, 2) / Rect(4, 3), Rect(0.24, 0.18))
|
|
self.assertRaises(TypeError, operator.truediv, Polar(4, 2), F(2, 3))
|
|
self.assertTypedEquals(Rect(4, 3) / F(2, 3), 6.0 + 4.5j)
|
|
self.assertEqual(F(3, 2) / SymbolicComplex('X'), SymbolicComplex('3/2 / X'))
|
|
self.assertRaises(TypeError, operator.truediv, SymbolicComplex('X'), F(3, 2))
|
|
|
|
self.assertEqual(F(3, 2) / Symbolic('X'), Symbolic('3/2 / X'))
|
|
self.assertRaises(TypeError, operator.truediv, Symbolic('X'), F(2, 3))
|
|
|
|
def testMixedIntegerDivision(self):
|
|
self.assertTypedEquals(0, F(1, 10) // 1)
|
|
self.assertTypedEquals(0.0, F(1, 10) // 1.0)
|
|
self.assertTypedEquals(10, 1 // F(1, 10))
|
|
self.assertTypedEquals(10**23, 10**22 // F(1, 10))
|
|
self.assertTypedEquals(1.0 // 0.1, 1.0 // F(1, 10))
|
|
|
|
self.assertTypedEquals(F(1, 10), F(1, 10) % 1)
|
|
self.assertTypedEquals(0.1, F(1, 10) % 1.0)
|
|
self.assertTypedEquals(F(0, 1), 1 % F(1, 10))
|
|
self.assertTypedEquals(1.0 % 0.1, 1.0 % F(1, 10))
|
|
self.assertTypedEquals(0.1, F(1, 10) % float('inf'))
|
|
self.assertTypedEquals(float('-inf'), F(1, 10) % float('-inf'))
|
|
self.assertTypedEquals(float('inf'), F(-1, 10) % float('inf'))
|
|
self.assertTypedEquals(-0.1, F(-1, 10) % float('-inf'))
|
|
|
|
self.assertTypedTupleEquals((0, F(1, 10)), divmod(F(1, 10), 1))
|
|
self.assertTypedTupleEquals(divmod(0.1, 1.0), divmod(F(1, 10), 1.0))
|
|
self.assertTypedTupleEquals((10, F(0)), divmod(1, F(1, 10)))
|
|
self.assertTypedTupleEquals(divmod(1.0, 0.1), divmod(1.0, F(1, 10)))
|
|
self.assertTypedTupleEquals(divmod(0.1, float('inf')), divmod(F(1, 10), float('inf')))
|
|
self.assertTypedTupleEquals(divmod(0.1, float('-inf')), divmod(F(1, 10), float('-inf')))
|
|
self.assertTypedTupleEquals(divmod(-0.1, float('inf')), divmod(F(-1, 10), float('inf')))
|
|
self.assertTypedTupleEquals(divmod(-0.1, float('-inf')), divmod(F(-1, 10), float('-inf')))
|
|
|
|
self.assertTypedEquals(F(3, 2) % DummyFraction(3, 5), F(3, 10))
|
|
self.assertTypedEquals(DummyFraction(5, 3) % F(2, 3), F(1, 3))
|
|
self.assertTypedEquals(F(3, 2) % Rat(3, 5), Rat(3, 6))
|
|
self.assertTypedEquals(Rat(5, 3) % F(2, 3), F(1, 3))
|
|
|
|
self.assertRaises(TypeError, operator.mod, F(2, 3), Root(4))
|
|
self.assertTypedEquals(Root(4) % F(3, 2), 0.5)
|
|
self.assertEqual(F(3, 2) % SymbolicReal('X'), SymbolicReal('3/2 % X'))
|
|
self.assertRaises(TypeError, operator.mod, SymbolicReal('X'), F(3, 2))
|
|
|
|
self.assertRaises(TypeError, operator.mod, F(3, 2), Polar(4, 2))
|
|
self.assertRaises(TypeError, operator.mod, F(3, 2), RectComplex(4, 3))
|
|
self.assertRaises(TypeError, operator.mod, Rect(4, 3), F(2, 3))
|
|
self.assertEqual(F(3, 2) % SymbolicComplex('X'), SymbolicComplex('3/2 % X'))
|
|
self.assertRaises(TypeError, operator.mod, SymbolicComplex('X'), F(3, 2))
|
|
|
|
self.assertEqual(F(3, 2) % Symbolic('X'), Symbolic('3/2 % X'))
|
|
self.assertRaises(TypeError, operator.mod, Symbolic('X'), F(2, 3))
|
|
|
|
def testMixedPower(self):
|
|
# ** has more interesting conversion rules.
|
|
self.assertTypedEquals(F(100, 1), F(1, 10) ** -2)
|
|
self.assertTypedEquals(F(100, 1), F(10, 1) ** 2)
|
|
self.assertTypedEquals(0.1, F(1, 10) ** 1.0)
|
|
self.assertTypedEquals(0.1 + 0j, F(1, 10) ** (1.0 + 0j))
|
|
self.assertTypedEquals(4 , 2 ** F(2, 1))
|
|
z = pow(-1, F(1, 2))
|
|
self.assertAlmostEqual(0, z.real)
|
|
self.assertEqual(1, z.imag)
|
|
self.assertTypedEquals(F(1, 4) , 2 ** F(-2, 1))
|
|
self.assertTypedEquals(2.0 , 4 ** F(1, 2))
|
|
self.assertTypedEquals(0.25, 2.0 ** F(-2, 1))
|
|
self.assertTypedEquals(1.0 + 0j, (1.0 + 0j) ** F(1, 10))
|
|
self.assertRaises(ZeroDivisionError, operator.pow,
|
|
F(0, 1), -2)
|
|
|
|
self.assertTypedEquals(F(3, 2) ** Rat(3, 1), F(27, 8))
|
|
self.assertTypedEquals(F(3, 2) ** Rat(-3, 1), F(8, 27))
|
|
self.assertTypedEquals(F(-3, 2) ** Rat(-3, 1), F(-8, 27))
|
|
self.assertTypedEquals(F(9, 4) ** Rat(3, 2), 3.375)
|
|
self.assertIsInstance(F(4, 9) ** Rat(-3, 2), float)
|
|
self.assertAlmostEqual(F(4, 9) ** Rat(-3, 2), 3.375)
|
|
self.assertAlmostEqual(F(-4, 9) ** Rat(-3, 2), 3.375j)
|
|
self.assertTypedEquals(Rat(9, 4) ** F(3, 2), 3.375)
|
|
self.assertTypedEquals(Rat(3, 2) ** F(3, 1), Rat(27, 8))
|
|
self.assertTypedEquals(Rat(3, 2) ** F(-3, 1), F(8, 27))
|
|
self.assertIsInstance(Rat(4, 9) ** F(-3, 2), float)
|
|
self.assertAlmostEqual(Rat(4, 9) ** F(-3, 2), 3.375)
|
|
|
|
self.assertTypedEquals(Root(4) ** F(2, 3), Root(4, 3.0))
|
|
self.assertTypedEquals(Root(4) ** F(2, 1), Root(4, F(1)))
|
|
self.assertTypedEquals(Root(4) ** F(-2, 1), Root(4, -F(1)))
|
|
self.assertTypedEquals(Root(4) ** F(-2, 3), Root(4, -3.0))
|
|
self.assertEqual(F(3, 2) ** SymbolicReal('X'), SymbolicReal('3/2 ** X'))
|
|
self.assertEqual(SymbolicReal('X') ** F(3, 2), SymbolicReal('X ** 1.5'))
|
|
|
|
self.assertTypedEquals(F(3, 2) ** Rect(2, 0), Polar(F(9,4), 0.0))
|
|
self.assertTypedEquals(F(1, 1) ** Rect(2, 3), Polar(F(1), 0.0))
|
|
self.assertTypedEquals(F(3, 2) ** RectComplex(2, 0), Polar(2.25, 0.0))
|
|
self.assertTypedEquals(F(1, 1) ** RectComplex(2, 3), Polar(1.0, 0.0))
|
|
self.assertTypedEquals(Polar(4, 2) ** F(3, 2), Polar(8.0, 3.0))
|
|
self.assertTypedEquals(Polar(4, 2) ** F(3, 1), Polar(64, 6))
|
|
self.assertTypedEquals(Polar(4, 2) ** F(-3, 1), Polar(0.015625, -6))
|
|
self.assertTypedEquals(Polar(4, 2) ** F(-3, 2), Polar(0.125, -3.0))
|
|
self.assertEqual(F(3, 2) ** SymbolicComplex('X'), SymbolicComplex('3/2 ** X'))
|
|
self.assertEqual(SymbolicComplex('X') ** F(3, 2), SymbolicComplex('X ** 1.5'))
|
|
|
|
self.assertEqual(F(3, 2) ** Symbolic('X'), Symbolic('3/2 ** X'))
|
|
self.assertEqual(Symbolic('X') ** F(3, 2), Symbolic('X ** 1.5'))
|
|
|
|
def testMixingWithDecimal(self):
|
|
# Decimal refuses mixed arithmetic (but not mixed comparisons)
|
|
self.assertRaises(TypeError, operator.add,
|
|
F(3,11), Decimal('3.1415926'))
|
|
self.assertRaises(TypeError, operator.add,
|
|
Decimal('3.1415926'), F(3,11))
|
|
|
|
def testComparisons(self):
|
|
self.assertTrue(F(1, 2) < F(2, 3))
|
|
self.assertFalse(F(1, 2) < F(1, 2))
|
|
self.assertTrue(F(1, 2) <= F(2, 3))
|
|
self.assertTrue(F(1, 2) <= F(1, 2))
|
|
self.assertFalse(F(2, 3) <= F(1, 2))
|
|
self.assertTrue(F(1, 2) == F(1, 2))
|
|
self.assertFalse(F(1, 2) == F(1, 3))
|
|
self.assertFalse(F(1, 2) != F(1, 2))
|
|
self.assertTrue(F(1, 2) != F(1, 3))
|
|
|
|
def testComparisonsDummyRational(self):
|
|
self.assertTrue(F(1, 2) == DummyRational(1, 2))
|
|
self.assertTrue(DummyRational(1, 2) == F(1, 2))
|
|
self.assertFalse(F(1, 2) == DummyRational(3, 4))
|
|
self.assertFalse(DummyRational(3, 4) == F(1, 2))
|
|
|
|
self.assertTrue(F(1, 2) < DummyRational(3, 4))
|
|
self.assertFalse(F(1, 2) < DummyRational(1, 2))
|
|
self.assertFalse(F(1, 2) < DummyRational(1, 7))
|
|
self.assertFalse(F(1, 2) > DummyRational(3, 4))
|
|
self.assertFalse(F(1, 2) > DummyRational(1, 2))
|
|
self.assertTrue(F(1, 2) > DummyRational(1, 7))
|
|
self.assertTrue(F(1, 2) <= DummyRational(3, 4))
|
|
self.assertTrue(F(1, 2) <= DummyRational(1, 2))
|
|
self.assertFalse(F(1, 2) <= DummyRational(1, 7))
|
|
self.assertFalse(F(1, 2) >= DummyRational(3, 4))
|
|
self.assertTrue(F(1, 2) >= DummyRational(1, 2))
|
|
self.assertTrue(F(1, 2) >= DummyRational(1, 7))
|
|
|
|
self.assertTrue(DummyRational(1, 2) < F(3, 4))
|
|
self.assertFalse(DummyRational(1, 2) < F(1, 2))
|
|
self.assertFalse(DummyRational(1, 2) < F(1, 7))
|
|
self.assertFalse(DummyRational(1, 2) > F(3, 4))
|
|
self.assertFalse(DummyRational(1, 2) > F(1, 2))
|
|
self.assertTrue(DummyRational(1, 2) > F(1, 7))
|
|
self.assertTrue(DummyRational(1, 2) <= F(3, 4))
|
|
self.assertTrue(DummyRational(1, 2) <= F(1, 2))
|
|
self.assertFalse(DummyRational(1, 2) <= F(1, 7))
|
|
self.assertFalse(DummyRational(1, 2) >= F(3, 4))
|
|
self.assertTrue(DummyRational(1, 2) >= F(1, 2))
|
|
self.assertTrue(DummyRational(1, 2) >= F(1, 7))
|
|
|
|
def testComparisonsDummyFloat(self):
|
|
x = DummyFloat(1./3.)
|
|
y = F(1, 3)
|
|
self.assertTrue(x != y)
|
|
self.assertTrue(x < y or x > y)
|
|
self.assertFalse(x == y)
|
|
self.assertFalse(x <= y and x >= y)
|
|
self.assertTrue(y != x)
|
|
self.assertTrue(y < x or y > x)
|
|
self.assertFalse(y == x)
|
|
self.assertFalse(y <= x and y >= x)
|
|
|
|
def testMixedLess(self):
|
|
self.assertTrue(2 < F(5, 2))
|
|
self.assertFalse(2 < F(4, 2))
|
|
self.assertTrue(F(5, 2) < 3)
|
|
self.assertFalse(F(4, 2) < 2)
|
|
|
|
self.assertTrue(F(1, 2) < 0.6)
|
|
self.assertFalse(F(1, 2) < 0.4)
|
|
self.assertTrue(0.4 < F(1, 2))
|
|
self.assertFalse(0.5 < F(1, 2))
|
|
|
|
self.assertFalse(float('inf') < F(1, 2))
|
|
self.assertTrue(float('-inf') < F(0, 10))
|
|
self.assertFalse(float('nan') < F(-3, 7))
|
|
self.assertTrue(F(1, 2) < float('inf'))
|
|
self.assertFalse(F(17, 12) < float('-inf'))
|
|
self.assertFalse(F(144, -89) < float('nan'))
|
|
|
|
def testMixedLessEqual(self):
|
|
self.assertTrue(0.5 <= F(1, 2))
|
|
self.assertFalse(0.6 <= F(1, 2))
|
|
self.assertTrue(F(1, 2) <= 0.5)
|
|
self.assertFalse(F(1, 2) <= 0.4)
|
|
self.assertTrue(2 <= F(4, 2))
|
|
self.assertFalse(2 <= F(3, 2))
|
|
self.assertTrue(F(4, 2) <= 2)
|
|
self.assertFalse(F(5, 2) <= 2)
|
|
|
|
self.assertFalse(float('inf') <= F(1, 2))
|
|
self.assertTrue(float('-inf') <= F(0, 10))
|
|
self.assertFalse(float('nan') <= F(-3, 7))
|
|
self.assertTrue(F(1, 2) <= float('inf'))
|
|
self.assertFalse(F(17, 12) <= float('-inf'))
|
|
self.assertFalse(F(144, -89) <= float('nan'))
|
|
|
|
def testBigFloatComparisons(self):
|
|
# Because 10**23 can't be represented exactly as a float:
|
|
self.assertFalse(F(10**23) == float(10**23))
|
|
# The first test demonstrates why these are important.
|
|
self.assertFalse(1e23 < float(F(math.trunc(1e23) + 1)))
|
|
self.assertTrue(1e23 < F(math.trunc(1e23) + 1))
|
|
self.assertFalse(1e23 <= F(math.trunc(1e23) - 1))
|
|
self.assertTrue(1e23 > F(math.trunc(1e23) - 1))
|
|
self.assertFalse(1e23 >= F(math.trunc(1e23) + 1))
|
|
|
|
def testBigComplexComparisons(self):
|
|
self.assertFalse(F(10**23) == complex(10**23))
|
|
self.assertRaises(TypeError, operator.gt, F(10**23), complex(10**23))
|
|
self.assertRaises(TypeError, operator.le, F(10**23), complex(10**23))
|
|
|
|
x = F(3, 8)
|
|
z = complex(0.375, 0.0)
|
|
w = complex(0.375, 0.2)
|
|
self.assertTrue(x == z)
|
|
self.assertFalse(x != z)
|
|
self.assertFalse(x == w)
|
|
self.assertTrue(x != w)
|
|
for op in operator.lt, operator.le, operator.gt, operator.ge:
|
|
self.assertRaises(TypeError, op, x, z)
|
|
self.assertRaises(TypeError, op, z, x)
|
|
self.assertRaises(TypeError, op, x, w)
|
|
self.assertRaises(TypeError, op, w, x)
|
|
|
|
def testMixedEqual(self):
|
|
self.assertTrue(0.5 == F(1, 2))
|
|
self.assertFalse(0.6 == F(1, 2))
|
|
self.assertTrue(F(1, 2) == 0.5)
|
|
self.assertFalse(F(1, 2) == 0.4)
|
|
self.assertTrue(2 == F(4, 2))
|
|
self.assertFalse(2 == F(3, 2))
|
|
self.assertTrue(F(4, 2) == 2)
|
|
self.assertFalse(F(5, 2) == 2)
|
|
self.assertFalse(F(5, 2) == float('nan'))
|
|
self.assertFalse(float('nan') == F(3, 7))
|
|
self.assertFalse(F(5, 2) == float('inf'))
|
|
self.assertFalse(float('-inf') == F(2, 5))
|
|
|
|
def testStringification(self):
|
|
self.assertEqual("Fraction(7, 3)", repr(F(7, 3)))
|
|
self.assertEqual("Fraction(6283185307, 2000000000)",
|
|
repr(F('3.1415926535')))
|
|
self.assertEqual("Fraction(-1, 100000000000000000000)",
|
|
repr(F(1, -10**20)))
|
|
self.assertEqual("7/3", str(F(7, 3)))
|
|
self.assertEqual("7", str(F(7, 1)))
|
|
|
|
def testHash(self):
|
|
hmod = sys.hash_info.modulus
|
|
hinf = sys.hash_info.inf
|
|
self.assertEqual(hash(2.5), hash(F(5, 2)))
|
|
self.assertEqual(hash(10**50), hash(F(10**50)))
|
|
self.assertNotEqual(hash(float(10**23)), hash(F(10**23)))
|
|
self.assertEqual(hinf, hash(F(1, hmod)))
|
|
# Check that __hash__ produces the same value as hash(), for
|
|
# consistency with int and Decimal. (See issue #10356.)
|
|
self.assertEqual(hash(F(-1)), F(-1).__hash__())
|
|
|
|
def testApproximatePi(self):
|
|
# Algorithm borrowed from
|
|
# http://docs.python.org/lib/decimal-recipes.html
|
|
three = F(3)
|
|
lasts, t, s, n, na, d, da = 0, three, 3, 1, 0, 0, 24
|
|
while abs(s - lasts) > F(1, 10**9):
|
|
lasts = s
|
|
n, na = n+na, na+8
|
|
d, da = d+da, da+32
|
|
t = (t * n) / d
|
|
s += t
|
|
self.assertAlmostEqual(math.pi, s)
|
|
|
|
def testApproximateCos1(self):
|
|
# Algorithm borrowed from
|
|
# http://docs.python.org/lib/decimal-recipes.html
|
|
x = F(1)
|
|
i, lasts, s, fact, num, sign = 0, 0, F(1), 1, 1, 1
|
|
while abs(s - lasts) > F(1, 10**9):
|
|
lasts = s
|
|
i += 2
|
|
fact *= i * (i-1)
|
|
num *= x * x
|
|
sign *= -1
|
|
s += num / fact * sign
|
|
self.assertAlmostEqual(math.cos(1), s)
|
|
|
|
def test_copy_deepcopy_pickle(self):
|
|
r = F(13, 7)
|
|
dr = DummyFraction(13, 7)
|
|
for proto in range(0, pickle.HIGHEST_PROTOCOL + 1):
|
|
self.assertEqual(r, loads(dumps(r, proto)))
|
|
self.assertEqual(id(r), id(copy(r)))
|
|
self.assertEqual(id(r), id(deepcopy(r)))
|
|
self.assertNotEqual(id(dr), id(copy(dr)))
|
|
self.assertNotEqual(id(dr), id(deepcopy(dr)))
|
|
self.assertTypedEquals(dr, copy(dr))
|
|
self.assertTypedEquals(dr, deepcopy(dr))
|
|
|
|
def test_slots(self):
|
|
# Issue 4998
|
|
r = F(13, 7)
|
|
self.assertRaises(AttributeError, setattr, r, 'a', 10)
|
|
|
|
def test_int_subclass(self):
|
|
class myint(int):
|
|
def __mul__(self, other):
|
|
return type(self)(int(self) * int(other))
|
|
def __floordiv__(self, other):
|
|
return type(self)(int(self) // int(other))
|
|
def __mod__(self, other):
|
|
x = type(self)(int(self) % int(other))
|
|
return x
|
|
@property
|
|
def numerator(self):
|
|
return type(self)(int(self))
|
|
@property
|
|
def denominator(self):
|
|
return type(self)(1)
|
|
|
|
f = fractions.Fraction(myint(1 * 3), myint(2 * 3))
|
|
self.assertEqual(f.numerator, 1)
|
|
self.assertEqual(f.denominator, 2)
|
|
self.assertEqual(type(f.numerator), myint)
|
|
self.assertEqual(type(f.denominator), myint)
|
|
|
|
def test_format_no_presentation_type(self):
|
|
# Triples (fraction, specification, expected_result).
|
|
testcases = [
|
|
# Explicit sign handling
|
|
(F(2, 3), '+', '+2/3'),
|
|
(F(-2, 3), '+', '-2/3'),
|
|
(F(3), '+', '+3'),
|
|
(F(-3), '+', '-3'),
|
|
(F(2, 3), ' ', ' 2/3'),
|
|
(F(-2, 3), ' ', '-2/3'),
|
|
(F(3), ' ', ' 3'),
|
|
(F(-3), ' ', '-3'),
|
|
(F(2, 3), '-', '2/3'),
|
|
(F(-2, 3), '-', '-2/3'),
|
|
(F(3), '-', '3'),
|
|
(F(-3), '-', '-3'),
|
|
# Padding
|
|
(F(0), '5', ' 0'),
|
|
(F(2, 3), '5', ' 2/3'),
|
|
(F(-2, 3), '5', ' -2/3'),
|
|
(F(2, 3), '0', '2/3'),
|
|
(F(2, 3), '1', '2/3'),
|
|
(F(2, 3), '2', '2/3'),
|
|
# Alignment
|
|
(F(2, 3), '<5', '2/3 '),
|
|
(F(2, 3), '>5', ' 2/3'),
|
|
(F(2, 3), '^5', ' 2/3 '),
|
|
(F(2, 3), '=5', ' 2/3'),
|
|
(F(-2, 3), '<5', '-2/3 '),
|
|
(F(-2, 3), '>5', ' -2/3'),
|
|
(F(-2, 3), '^5', '-2/3 '),
|
|
(F(-2, 3), '=5', '- 2/3'),
|
|
# Fill
|
|
(F(2, 3), 'X>5', 'XX2/3'),
|
|
(F(-2, 3), '.<5', '-2/3.'),
|
|
(F(-2, 3), '\n^6', '\n-2/3\n'),
|
|
# Thousands separators
|
|
(F(1234, 5679), ',', '1,234/5,679'),
|
|
(F(-1234, 5679), '_', '-1_234/5_679'),
|
|
(F(1234567), '_', '1_234_567'),
|
|
(F(-1234567), ',', '-1,234,567'),
|
|
# Alternate form forces a slash in the output
|
|
(F(123), '#', '123/1'),
|
|
(F(-123), '#', '-123/1'),
|
|
(F(0), '#', '0/1'),
|
|
]
|
|
for fraction, spec, expected in testcases:
|
|
with self.subTest(fraction=fraction, spec=spec):
|
|
self.assertEqual(format(fraction, spec), expected)
|
|
|
|
def test_format_e_presentation_type(self):
|
|
# Triples (fraction, specification, expected_result)
|
|
testcases = [
|
|
(F(2, 3), '.6e', '6.666667e-01'),
|
|
(F(3, 2), '.6e', '1.500000e+00'),
|
|
(F(2, 13), '.6e', '1.538462e-01'),
|
|
(F(2, 23), '.6e', '8.695652e-02'),
|
|
(F(2, 33), '.6e', '6.060606e-02'),
|
|
(F(13, 2), '.6e', '6.500000e+00'),
|
|
(F(20, 2), '.6e', '1.000000e+01'),
|
|
(F(23, 2), '.6e', '1.150000e+01'),
|
|
(F(33, 2), '.6e', '1.650000e+01'),
|
|
(F(2, 3), '.6e', '6.666667e-01'),
|
|
(F(3, 2), '.6e', '1.500000e+00'),
|
|
# Zero
|
|
(F(0), '.3e', '0.000e+00'),
|
|
# Powers of 10, to exercise the log10 boundary logic
|
|
(F(1, 1000), '.3e', '1.000e-03'),
|
|
(F(1, 100), '.3e', '1.000e-02'),
|
|
(F(1, 10), '.3e', '1.000e-01'),
|
|
(F(1, 1), '.3e', '1.000e+00'),
|
|
(F(10), '.3e', '1.000e+01'),
|
|
(F(100), '.3e', '1.000e+02'),
|
|
(F(1000), '.3e', '1.000e+03'),
|
|
# Boundary where we round up to the next power of 10
|
|
(F('99.999994999999'), '.6e', '9.999999e+01'),
|
|
(F('99.999995'), '.6e', '1.000000e+02'),
|
|
(F('99.999995000001'), '.6e', '1.000000e+02'),
|
|
# Negatives
|
|
(F(-2, 3), '.6e', '-6.666667e-01'),
|
|
(F(-3, 2), '.6e', '-1.500000e+00'),
|
|
(F(-100), '.6e', '-1.000000e+02'),
|
|
# Large and small
|
|
(F('1e1000'), '.3e', '1.000e+1000'),
|
|
(F('1e-1000'), '.3e', '1.000e-1000'),
|
|
# Using 'E' instead of 'e' should give us a capital 'E'
|
|
(F(2, 3), '.6E', '6.666667E-01'),
|
|
# Tiny precision
|
|
(F(2, 3), '.1e', '6.7e-01'),
|
|
(F('0.995'), '.0e', '1e+00'),
|
|
# Default precision is 6
|
|
(F(22, 7), 'e', '3.142857e+00'),
|
|
# Alternate form forces a decimal point
|
|
(F('0.995'), '#.0e', '1.e+00'),
|
|
# Check that padding takes the exponent into account.
|
|
(F(22, 7), '11.6e', '3.142857e+00'),
|
|
(F(22, 7), '12.6e', '3.142857e+00'),
|
|
(F(22, 7), '13.6e', ' 3.142857e+00'),
|
|
# Thousands separators
|
|
(F('1234567.123456'), ',.5e', '1.23457e+06'),
|
|
(F('123.123456'), '012_.2e', '0_001.23e+02'),
|
|
# z flag is legal, but never makes a difference to the output
|
|
(F(-1, 7**100), 'z.6e', '-3.091690e-85'),
|
|
]
|
|
for fraction, spec, expected in testcases:
|
|
with self.subTest(fraction=fraction, spec=spec):
|
|
self.assertEqual(format(fraction, spec), expected)
|
|
|
|
def test_format_f_presentation_type(self):
|
|
# Triples (fraction, specification, expected_result)
|
|
testcases = [
|
|
# Simple .f formatting
|
|
(F(0, 1), '.2f', '0.00'),
|
|
(F(1, 3), '.2f', '0.33'),
|
|
(F(2, 3), '.2f', '0.67'),
|
|
(F(4, 3), '.2f', '1.33'),
|
|
(F(1, 8), '.2f', '0.12'),
|
|
(F(3, 8), '.2f', '0.38'),
|
|
(F(1, 13), '.2f', '0.08'),
|
|
(F(1, 199), '.2f', '0.01'),
|
|
(F(1, 200), '.2f', '0.00'),
|
|
(F(22, 7), '.5f', '3.14286'),
|
|
(F('399024789'), '.2f', '399024789.00'),
|
|
# Large precision (more than float can provide)
|
|
(F(104348, 33215), '.50f',
|
|
'3.14159265392142104470871594159265392142104470871594'),
|
|
# Precision defaults to 6 if not given
|
|
(F(22, 7), 'f', '3.142857'),
|
|
(F(0), 'f', '0.000000'),
|
|
(F(-22, 7), 'f', '-3.142857'),
|
|
# Round-ties-to-even checks
|
|
(F('1.225'), '.2f', '1.22'),
|
|
(F('1.2250000001'), '.2f', '1.23'),
|
|
(F('1.2349999999'), '.2f', '1.23'),
|
|
(F('1.235'), '.2f', '1.24'),
|
|
(F('1.245'), '.2f', '1.24'),
|
|
(F('1.2450000001'), '.2f', '1.25'),
|
|
(F('1.2549999999'), '.2f', '1.25'),
|
|
(F('1.255'), '.2f', '1.26'),
|
|
(F('-1.225'), '.2f', '-1.22'),
|
|
(F('-1.2250000001'), '.2f', '-1.23'),
|
|
(F('-1.2349999999'), '.2f', '-1.23'),
|
|
(F('-1.235'), '.2f', '-1.24'),
|
|
(F('-1.245'), '.2f', '-1.24'),
|
|
(F('-1.2450000001'), '.2f', '-1.25'),
|
|
(F('-1.2549999999'), '.2f', '-1.25'),
|
|
(F('-1.255'), '.2f', '-1.26'),
|
|
# Negatives and sign handling
|
|
(F(2, 3), '.2f', '0.67'),
|
|
(F(2, 3), '-.2f', '0.67'),
|
|
(F(2, 3), '+.2f', '+0.67'),
|
|
(F(2, 3), ' .2f', ' 0.67'),
|
|
(F(-2, 3), '.2f', '-0.67'),
|
|
(F(-2, 3), '-.2f', '-0.67'),
|
|
(F(-2, 3), '+.2f', '-0.67'),
|
|
(F(-2, 3), ' .2f', '-0.67'),
|
|
# Formatting to zero places
|
|
(F(1, 2), '.0f', '0'),
|
|
(F(-1, 2), '.0f', '-0'),
|
|
(F(22, 7), '.0f', '3'),
|
|
(F(-22, 7), '.0f', '-3'),
|
|
# Formatting to zero places, alternate form
|
|
(F(1, 2), '#.0f', '0.'),
|
|
(F(-1, 2), '#.0f', '-0.'),
|
|
(F(22, 7), '#.0f', '3.'),
|
|
(F(-22, 7), '#.0f', '-3.'),
|
|
# z flag for suppressing negative zeros
|
|
(F('-0.001'), 'z.2f', '0.00'),
|
|
(F('-0.001'), '-z.2f', '0.00'),
|
|
(F('-0.001'), '+z.2f', '+0.00'),
|
|
(F('-0.001'), ' z.2f', ' 0.00'),
|
|
(F('0.001'), 'z.2f', '0.00'),
|
|
(F('0.001'), '-z.2f', '0.00'),
|
|
(F('0.001'), '+z.2f', '+0.00'),
|
|
(F('0.001'), ' z.2f', ' 0.00'),
|
|
# Specifying a minimum width
|
|
(F(2, 3), '6.2f', ' 0.67'),
|
|
(F(12345), '6.2f', '12345.00'),
|
|
(F(12345), '12f', '12345.000000'),
|
|
# Fill and alignment
|
|
(F(2, 3), '>6.2f', ' 0.67'),
|
|
(F(2, 3), '<6.2f', '0.67 '),
|
|
(F(2, 3), '^3.2f', '0.67'),
|
|
(F(2, 3), '^4.2f', '0.67'),
|
|
(F(2, 3), '^5.2f', '0.67 '),
|
|
(F(2, 3), '^6.2f', ' 0.67 '),
|
|
(F(2, 3), '^7.2f', ' 0.67 '),
|
|
(F(2, 3), '^8.2f', ' 0.67 '),
|
|
# '=' alignment
|
|
(F(-2, 3), '=+8.2f', '- 0.67'),
|
|
(F(2, 3), '=+8.2f', '+ 0.67'),
|
|
# Fill character
|
|
(F(-2, 3), 'X>3.2f', '-0.67'),
|
|
(F(-2, 3), 'X>7.2f', 'XX-0.67'),
|
|
(F(-2, 3), 'X<7.2f', '-0.67XX'),
|
|
(F(-2, 3), 'X^7.2f', 'X-0.67X'),
|
|
(F(-2, 3), 'X=7.2f', '-XX0.67'),
|
|
(F(-2, 3), ' >7.2f', ' -0.67'),
|
|
# Corner cases: weird fill characters
|
|
(F(-2, 3), '\x00>7.2f', '\x00\x00-0.67'),
|
|
(F(-2, 3), '\n>7.2f', '\n\n-0.67'),
|
|
(F(-2, 3), '\t>7.2f', '\t\t-0.67'),
|
|
(F(-2, 3), '>>7.2f', '>>-0.67'),
|
|
(F(-2, 3), '<>7.2f', '<<-0.67'),
|
|
(F(-2, 3), '→>7.2f', '→→-0.67'),
|
|
# Zero-padding
|
|
(F(-2, 3), '07.2f', '-000.67'),
|
|
(F(-2, 3), '-07.2f', '-000.67'),
|
|
(F(2, 3), '+07.2f', '+000.67'),
|
|
(F(2, 3), ' 07.2f', ' 000.67'),
|
|
# An isolated zero is a minimum width, not a zero-pad flag.
|
|
# So unlike zero-padding, it's legal in combination with alignment.
|
|
(F(2, 3), '0.2f', '0.67'),
|
|
(F(2, 3), '>0.2f', '0.67'),
|
|
(F(2, 3), '<0.2f', '0.67'),
|
|
(F(2, 3), '^0.2f', '0.67'),
|
|
(F(2, 3), '=0.2f', '0.67'),
|
|
# Corner case: zero-padding _and_ a zero minimum width.
|
|
(F(2, 3), '00.2f', '0.67'),
|
|
# Thousands separator (only affects portion before the point)
|
|
(F(2, 3), ',.2f', '0.67'),
|
|
(F(2, 3), ',.7f', '0.6666667'),
|
|
(F('123456.789'), ',.2f', '123,456.79'),
|
|
(F('1234567'), ',.2f', '1,234,567.00'),
|
|
(F('12345678'), ',.2f', '12,345,678.00'),
|
|
(F('12345678'), ',f', '12,345,678.000000'),
|
|
# Underscore as thousands separator
|
|
(F(2, 3), '_.2f', '0.67'),
|
|
(F(2, 3), '_.7f', '0.6666667'),
|
|
(F('123456.789'), '_.2f', '123_456.79'),
|
|
(F('1234567'), '_.2f', '1_234_567.00'),
|
|
(F('12345678'), '_.2f', '12_345_678.00'),
|
|
# Thousands and zero-padding
|
|
(F('1234.5678'), '07,.2f', '1,234.57'),
|
|
(F('1234.5678'), '08,.2f', '1,234.57'),
|
|
(F('1234.5678'), '09,.2f', '01,234.57'),
|
|
(F('1234.5678'), '010,.2f', '001,234.57'),
|
|
(F('1234.5678'), '011,.2f', '0,001,234.57'),
|
|
(F('1234.5678'), '012,.2f', '0,001,234.57'),
|
|
(F('1234.5678'), '013,.2f', '00,001,234.57'),
|
|
(F('1234.5678'), '014,.2f', '000,001,234.57'),
|
|
(F('1234.5678'), '015,.2f', '0,000,001,234.57'),
|
|
(F('1234.5678'), '016,.2f', '0,000,001,234.57'),
|
|
(F('-1234.5678'), '07,.2f', '-1,234.57'),
|
|
(F('-1234.5678'), '08,.2f', '-1,234.57'),
|
|
(F('-1234.5678'), '09,.2f', '-1,234.57'),
|
|
(F('-1234.5678'), '010,.2f', '-01,234.57'),
|
|
(F('-1234.5678'), '011,.2f', '-001,234.57'),
|
|
(F('-1234.5678'), '012,.2f', '-0,001,234.57'),
|
|
(F('-1234.5678'), '013,.2f', '-0,001,234.57'),
|
|
(F('-1234.5678'), '014,.2f', '-00,001,234.57'),
|
|
(F('-1234.5678'), '015,.2f', '-000,001,234.57'),
|
|
(F('-1234.5678'), '016,.2f', '-0,000,001,234.57'),
|
|
# Corner case: no decimal point
|
|
(F('-1234.5678'), '06,.0f', '-1,235'),
|
|
(F('-1234.5678'), '07,.0f', '-01,235'),
|
|
(F('-1234.5678'), '08,.0f', '-001,235'),
|
|
(F('-1234.5678'), '09,.0f', '-0,001,235'),
|
|
# Corner-case - zero-padding specified through fill and align
|
|
# instead of the zero-pad character - in this case, treat '0' as a
|
|
# regular fill character and don't attempt to insert commas into
|
|
# the filled portion. This differs from the int and float
|
|
# behaviour.
|
|
(F('1234.5678'), '0=12,.2f', '00001,234.57'),
|
|
# Corner case where it's not clear whether the '0' indicates zero
|
|
# padding or gives the minimum width, but there's still an obvious
|
|
# answer to give. We want this to work in case the minimum width
|
|
# is being inserted programmatically: spec = f'{width}.2f'.
|
|
(F('12.34'), '0.2f', '12.34'),
|
|
(F('12.34'), 'X>0.2f', '12.34'),
|
|
# 'F' should work identically to 'f'
|
|
(F(22, 7), '.5F', '3.14286'),
|
|
# %-specifier
|
|
(F(22, 7), '.2%', '314.29%'),
|
|
(F(1, 7), '.2%', '14.29%'),
|
|
(F(1, 70), '.2%', '1.43%'),
|
|
(F(1, 700), '.2%', '0.14%'),
|
|
(F(1, 7000), '.2%', '0.01%'),
|
|
(F(1, 70000), '.2%', '0.00%'),
|
|
(F(1, 7), '.0%', '14%'),
|
|
(F(1, 7), '#.0%', '14.%'),
|
|
(F(100, 7), ',.2%', '1,428.57%'),
|
|
(F(22, 7), '7.2%', '314.29%'),
|
|
(F(22, 7), '8.2%', ' 314.29%'),
|
|
(F(22, 7), '08.2%', '0314.29%'),
|
|
# Test cases from #67790 and discuss.python.org Ideas thread.
|
|
(F(1, 3), '.2f', '0.33'),
|
|
(F(1, 8), '.2f', '0.12'),
|
|
(F(3, 8), '.2f', '0.38'),
|
|
(F(2545, 1000), '.2f', '2.54'),
|
|
(F(2549, 1000), '.2f', '2.55'),
|
|
(F(2635, 1000), '.2f', '2.64'),
|
|
(F(1, 100), '.1f', '0.0'),
|
|
(F(49, 1000), '.1f', '0.0'),
|
|
(F(51, 1000), '.1f', '0.1'),
|
|
(F(149, 1000), '.1f', '0.1'),
|
|
(F(151, 1000), '.1f', '0.2'),
|
|
]
|
|
for fraction, spec, expected in testcases:
|
|
with self.subTest(fraction=fraction, spec=spec):
|
|
self.assertEqual(format(fraction, spec), expected)
|
|
|
|
def test_format_g_presentation_type(self):
|
|
# Triples (fraction, specification, expected_result)
|
|
testcases = [
|
|
(F('0.000012345678'), '.6g', '1.23457e-05'),
|
|
(F('0.00012345678'), '.6g', '0.000123457'),
|
|
(F('0.0012345678'), '.6g', '0.00123457'),
|
|
(F('0.012345678'), '.6g', '0.0123457'),
|
|
(F('0.12345678'), '.6g', '0.123457'),
|
|
(F('1.2345678'), '.6g', '1.23457'),
|
|
(F('12.345678'), '.6g', '12.3457'),
|
|
(F('123.45678'), '.6g', '123.457'),
|
|
(F('1234.5678'), '.6g', '1234.57'),
|
|
(F('12345.678'), '.6g', '12345.7'),
|
|
(F('123456.78'), '.6g', '123457'),
|
|
(F('1234567.8'), '.6g', '1.23457e+06'),
|
|
# Rounding up cases
|
|
(F('9.99999e+2'), '.4g', '1000'),
|
|
(F('9.99999e-8'), '.4g', '1e-07'),
|
|
(F('9.99999e+8'), '.4g', '1e+09'),
|
|
# Check round-ties-to-even behaviour
|
|
(F('-0.115'), '.2g', '-0.12'),
|
|
(F('-0.125'), '.2g', '-0.12'),
|
|
(F('-0.135'), '.2g', '-0.14'),
|
|
(F('-0.145'), '.2g', '-0.14'),
|
|
(F('0.115'), '.2g', '0.12'),
|
|
(F('0.125'), '.2g', '0.12'),
|
|
(F('0.135'), '.2g', '0.14'),
|
|
(F('0.145'), '.2g', '0.14'),
|
|
# Trailing zeros and decimal point suppressed by default ...
|
|
(F(0), '.6g', '0'),
|
|
(F('123.400'), '.6g', '123.4'),
|
|
(F('123.000'), '.6g', '123'),
|
|
(F('120.000'), '.6g', '120'),
|
|
(F('12000000'), '.6g', '1.2e+07'),
|
|
# ... but not when alternate form is in effect
|
|
(F(0), '#.6g', '0.00000'),
|
|
(F('123.400'), '#.6g', '123.400'),
|
|
(F('123.000'), '#.6g', '123.000'),
|
|
(F('120.000'), '#.6g', '120.000'),
|
|
(F('12000000'), '#.6g', '1.20000e+07'),
|
|
# 'G' format (uses 'E' instead of 'e' for the exponent indicator)
|
|
(F('123.45678'), '.6G', '123.457'),
|
|
(F('1234567.8'), '.6G', '1.23457E+06'),
|
|
# Default precision is 6 significant figures
|
|
(F('3.1415926535'), 'g', '3.14159'),
|
|
# Precision 0 is treated the same as precision 1.
|
|
(F('0.000031415'), '.0g', '3e-05'),
|
|
(F('0.00031415'), '.0g', '0.0003'),
|
|
(F('0.31415'), '.0g', '0.3'),
|
|
(F('3.1415'), '.0g', '3'),
|
|
(F('3.1415'), '#.0g', '3.'),
|
|
(F('31.415'), '.0g', '3e+01'),
|
|
(F('31.415'), '#.0g', '3.e+01'),
|
|
(F('0.000031415'), '.1g', '3e-05'),
|
|
(F('0.00031415'), '.1g', '0.0003'),
|
|
(F('0.31415'), '.1g', '0.3'),
|
|
(F('3.1415'), '.1g', '3'),
|
|
(F('3.1415'), '#.1g', '3.'),
|
|
(F('31.415'), '.1g', '3e+01'),
|
|
# Thousands separator
|
|
(F(2**64), '_.25g', '18_446_744_073_709_551_616'),
|
|
# As with 'e' format, z flag is legal, but has no effect
|
|
(F(-1, 7**100), 'zg', '-3.09169e-85'),
|
|
]
|
|
for fraction, spec, expected in testcases:
|
|
with self.subTest(fraction=fraction, spec=spec):
|
|
self.assertEqual(format(fraction, spec), expected)
|
|
|
|
def test_invalid_formats(self):
|
|
fraction = F(2, 3)
|
|
with self.assertRaises(TypeError):
|
|
format(fraction, None)
|
|
|
|
invalid_specs = [
|
|
'Q6f', # regression test
|
|
# illegal to use fill or alignment when zero padding
|
|
'X>010f',
|
|
'X<010f',
|
|
'X^010f',
|
|
'X=010f',
|
|
'0>010f',
|
|
'0<010f',
|
|
'0^010f',
|
|
'0=010f',
|
|
'>010f',
|
|
'<010f',
|
|
'^010f',
|
|
'=010e',
|
|
'=010f',
|
|
'=010g',
|
|
'=010%',
|
|
'>00.2f',
|
|
'>00f',
|
|
# Too many zeros - minimum width should not have leading zeros
|
|
'006f',
|
|
# Leading zeros in precision
|
|
'.010f',
|
|
'.02f',
|
|
'.000f',
|
|
# Missing precision
|
|
'.e',
|
|
'.f',
|
|
'.g',
|
|
'.%',
|
|
# Z instead of z for negative zero suppression
|
|
'Z.2f'
|
|
# z flag not supported for general formatting
|
|
'z',
|
|
# zero padding not supported for general formatting
|
|
'05',
|
|
]
|
|
for spec in invalid_specs:
|
|
with self.subTest(spec=spec):
|
|
with self.assertRaises(ValueError):
|
|
format(fraction, spec)
|
|
|
|
@requires_IEEE_754
|
|
def test_float_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()
|
|
if fmt == '%r':
|
|
continue
|
|
fmt2 = fmt[1:]
|
|
with self.subTest(fmt=fmt, arg=arg):
|
|
f = F(float(arg))
|
|
self.assertEqual(format(f, fmt2), rhs)
|
|
if f: # skip negative zero
|
|
self.assertEqual(format(-f, fmt2), '-' + rhs)
|
|
f = F(arg)
|
|
self.assertEqual(float(format(f, fmt2)), float(rhs))
|
|
self.assertEqual(float(format(-f, fmt2)), float('-' + rhs))
|
|
|
|
def test_complex_handling(self):
|
|
# See issue gh-102840 for more details.
|
|
|
|
a = F(1, 2)
|
|
b = 1j
|
|
message = "unsupported operand type(s) for %s: '%s' and '%s'"
|
|
# test forward
|
|
self.assertRaisesMessage(TypeError,
|
|
message % ("%", "Fraction", "complex"),
|
|
operator.mod, a, b)
|
|
self.assertRaisesMessage(TypeError,
|
|
message % ("//", "Fraction", "complex"),
|
|
operator.floordiv, a, b)
|
|
self.assertRaisesMessage(TypeError,
|
|
message % ("divmod()", "Fraction", "complex"),
|
|
divmod, a, b)
|
|
# test reverse
|
|
self.assertRaisesMessage(TypeError,
|
|
message % ("%", "complex", "Fraction"),
|
|
operator.mod, b, a)
|
|
self.assertRaisesMessage(TypeError,
|
|
message % ("//", "complex", "Fraction"),
|
|
operator.floordiv, b, a)
|
|
self.assertRaisesMessage(TypeError,
|
|
message % ("divmod()", "complex", "Fraction"),
|
|
divmod, b, a)
|
|
|
|
def test_three_argument_pow(self):
|
|
message = "unsupported operand type(s) for ** or pow(): '%s', '%s', '%s'"
|
|
self.assertRaisesMessage(TypeError,
|
|
message % ("Fraction", "int", "int"),
|
|
pow, F(3), 4, 5)
|
|
|
|
|
|
if __name__ == '__main__':
|
|
unittest.main()
|