Thread by @somacdivad

A Tale of Two NaNs (A #Python 🧵)

(Plus a bonus experiment in Twitter fonts that may end disastrously)

NaNs are annoying.

You can’t tell if they’re in a list:

>>> 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) 𝚒𝚗 [𝟷, 𝟸, 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”)]
𝙵𝚊𝚕𝚜𝚎

You can end up with more than one NaN in a set:

>>> 𝚂 = {𝟷, 𝟷, 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”), 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”)}
>>> 𝚂
{𝟷, 𝚗𝚊𝚗, 𝚗𝚊𝚗}

But they also aren’t 𝘪𝘯 the set:

>>> 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) 𝚒𝚗 𝚂
𝙵𝚊𝚕𝚜𝚎

And if a NaN winds up as a dictionary key, well… it’s lost to the abyss 🕳

>>> 𝚍 = {𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”): 𝟷}
>>> 𝚍
{𝚗𝚊𝚗: 𝟷}

>>> # 𝚁𝚊𝚒𝚜𝚎𝚜 𝙺𝚎𝚢𝙴𝚛𝚛𝚘𝚛
>>> 𝚍[𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”)]

(But you can keep adding NaN keys if you want to 🤫)

>>> 𝚍[𝚏𝚕𝚘𝚊𝚝("𝚗𝚊𝚗")] = 𝟸
>>> 𝚍[𝚏𝚕𝚘𝚊𝚝("𝚗𝚊𝚗")] = 𝟹
>>> 𝚍
{𝚗𝚊𝚗: 𝟷, 𝚗𝚊𝚗: 𝟸, 𝚗𝚊𝚗: 𝟹}

It’s all because of two key properties:

1️⃣ 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) is not equal to itself:

>>> 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) == 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”)
𝙵𝚊𝚕𝚜𝚎

2️⃣ 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) is not 𝐢𝐝𝐞𝐧𝐭𝐢𝐜𝐚𝐥* to itself:

>>> 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) 𝚒𝚜 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”)
𝙵𝚊𝚕𝚜𝚎

*Two Python objects are 𝐢𝐝𝐞𝐧𝐭𝐢𝐜𝐚𝐥 if they are located at the same memory address. Or, more precisely, the 𝚒𝚍() function returns the same value for both objects.

So what’s happening here?

Python checks two conditions when determining if an object is a member of a collection (i.e., list, set, dict keys):

1️⃣ Is the object identical to one of the objects in the collection?

2️⃣ Is the object equal (using ==) to an object in the collection?

If either one of those conditions is true, then the object is a member of the collection.

(See docs.python.org/3/reference/ex… if you want to nerd out over membership 🤓)

But neither of those conditions are ever true for 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”)!

That said, since 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) is a floating point value — and thus immutable — there’s no problem using 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) in a set or as a dictionary key.

I know, it can be kind of confusing.

Let’s add another NaN to the mix.

𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”) isn’t the only way to make a NaN object in Python.

No, I’m not talking about 𝚗𝚞𝚖𝚙𝚢.𝚗𝚊𝚗.

There’s also 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗:

>>> 𝚒𝚖𝚙𝚘𝚛𝚝 𝚖𝚊𝚝𝚑
>>> 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗
𝚗𝚊𝚗

𝚖𝚊𝚝𝚑.𝚗𝚊𝚗 was added to Python in version 3.5, and here’s what the docs say about it:

“A floating-point ‘not a number’ (NaN) value. Equivalent to the output of 𝚏𝚕𝚘𝚊𝚝(‘𝚗𝚊𝚗’).”

docs.python.org/3/library/math…

So, what do you think are the results of the following expressions?

1️⃣ 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗 == 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗

2️⃣ 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗 𝚒𝚜 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗

If you answered 𝙵𝚊𝚕𝚜𝚎 for 1️⃣, then congrats! You’re right! ✅

But if you also answered 𝙵𝚊𝚕𝚜𝚎 for 2️⃣, then you are incorrect ❌

Check out what happens when you use 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗 as a dictionary key:

>>> 𝚍 = {𝚖𝚊𝚝𝚑.𝚗𝚊𝚗: 𝟷}
>>> 𝚍[𝚖𝚊𝚝𝚑.𝚗𝚊𝚗]
𝟷

Sets also treat 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗 differently than 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”):

>>> {𝚖𝚊𝚝𝚑.𝚗𝚊𝚗, 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗, 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗}
{𝚗𝚊𝚗}

Who knows what’s going on here? What’s the difference between 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗 and 𝚏𝚕𝚘𝚊𝚝(“𝚗𝚊𝚗”)?

100 internet points to the first person with the right answer!

And if you want even more NaN craziness, check out the discussion thread from the Python issue tracker that led to the inclusion of 𝚖𝚊𝚝𝚑.𝚗𝚊𝚗.

For instance, did you know that there are 𝘴𝘪𝘨𝘯𝘦𝘥 NaNs? 🤯

bugs.python.org/issue23185