[英]Is Python's == an equivalence relation on the floats?
In native Python, without using NumPy (for which numpy.nan != numpy.nan
) there is no NaN, so am I right in thinking that Python's floating point ==
is reflexive? 在本机Python中,如果不使用NumPy(对于numpy.nan != numpy.nan
),则没有NaN,所以我认为Python的浮点==
具有反射性是对的吗? Then since it is symmetric ( a == b
implies b == a
) and transitive (if a==b
and b==c
then a==c
), can we say that Python's ==
is an equivalence relation on the float
s? 然后,由于它是对称的( a == b
意味着b == a
)并且是可传递的(如果a==b
和b==c
则a==c
),我们可以说Python的==
是float
上的等价关系s?
EDIT: OK, so I learned that there is a NaN: float('nan')
(thanks @unutbu) which will propagate through various operations, but does any native Python method return it (rather than raising an Exception) without me introducing it by this assignment? 编辑:好的,让我了解到有一个楠: float('nan')
感谢@unutbu)将通过各种操作传播,但是否有任何原生的Python方法返回它(而不是抛出一个异常),而我将其引入通过这项任务?
==
is reflexive for all numbers, zero, -zero, ininity, and -infinity, but not for nan. ==
对于所有数字(零,-零,ininity和-infinity)是自反的,但对于nan则不自反。
You can get inf
, -inf
, and nan
in native Python just by arithmetic operations on literals, like below. 您可以通过对文字进行算术运算来在本地Python中获得inf
, -inf
和nan
,如下所示。
These behave correctly, as in IEEE 754 and without math domain exception: 它们的行为正确,如在IEEE 754中并且没有数学域异常:
>>> 1e1000 == 1e1000
True
>>> 1e1000/1e1000 == 1e1000/1e1000
False
1e1000
is a very big number, so float and double represent it as an infinity. 1e1000
是一个非常大的数字,因此float和double将其表示为无穷大。
Floating-point arithmetic in Python also works OK for infinity minus infinity etc.: Python中的浮点算术对于无穷负无穷等也可以工作:
>>> x = 1e1000
>>> x
inf
>>> x+x
inf
>>> x-x
nan
>>> x*2
inf
>>> x == x
True
>>> x-x == x-x
False
>>>
And for the zero and minus zero case: 对于零和负零的情况:
>>> inf = float("inf")
>>> 1/inf
0.0
>>> -1/inf
-0.0
>>> -1/inf == 1/inf
True
>>>
float('nan')
exists in native Python and float('nan') != float('nan')
. float('nan')
存在于本机Python中,并且float('nan') != float('nan')
。 So no, ==
is not an equivalence relation since it lacks reflexivity: 所以不, ==
不是等价关系,因为它缺乏自反性:
In [40]: float('nan') == float('nan')
Out[40]: False
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