NaN

A Japanese contraction of the word nani, which corresponds to the English interrogative "what". There is no particular system for using nan versus nani, so you just have to learn the proper situations.

Sore wa nan desu ka.
What is that?

Nan ja.
What's going on? (abrupt, do not use)

Asa wa nan-ji ni okimashita ka.
What time did you wake up this morning?

Written nan, with the kanji for "what".

This is a song by Ween, from the album God Ween Satan: The Oneness.

Eddie Dingle does guest vocals on this song. The guitar is just a sort of stuttery accompaniment, nothing special, while Eddie just talks and slurs his words. No melody, just talking. Eddie talks in a really weird, slow, stuttery, syrupy voice. He giggles in the middle of the song like he's amusing himself and couldn't hold it in. In the beginning he introduces himself:

"Hi. I'm fuckin' Eddie Dingle. I got this girl named Nan. She overpopulated my senses. And then fucking dicked me over."

The "song" proper starts then:

what's your big secret?
could you give me a clue?
oh silly girl
i'm so in love with u.

There's a lot more of Eddie urging Nan to tell him what's on her mind and whatnot, and then he begins to get jealous of her other relationships, just beginning to rant without a script: "You know, I saw you yesterday walkin' with Danny. He's a fucker. And you're a fucker too, you know what you did to me baby? Yeah, you know what you did, and now you're walkin' with Danny down the street, how that make me feel huh? How you think that makes me feel huh? Huh? You think I like it here you fucker? You fuckin' bitch, I hate you you fucker, you keep walkin' with Danny, you keep fuckin' walkin' with Danny, I don't give a fuck, yeah I don't give a flyin' fuck about you or Danny you bitch!"

Nice note on which to end a song, eh? That transcription is not anywhere in the lyrics, it's just a random rant. But I do believe he's lying somewhere in there . . . can't you tell Eddie still loves Nan? What a storybook romance.

Incidentally, Eddie Dingle may be the subject of the completely instrumental "A Tear for Eddie" on the Ween album Chocolate and Cheese.

This song is © 1990 by Ween, Twin/Tone records.

Next song on this album: Licking the Palm for Guava

A term commonly used among actors.

NAN= No Acting Necessary.

Usually when an egotistical actor or actress is upset over the small walk-on or cameo, or a quick shot in a music video. You don't even say a word usually, like a prop.

In Britain at least, 'Nan' is the most informal way of referring to your grandmother.

The IEEE 754 binary floating point arithmetic standard states that the default value¹ for an invalid operation is a NaN or a Not-a-Number.

SIDEBAR: IEEE 754 also states that if the result of a computation is too large to be represented in the precision being used then it is to be replaced by an infinity and that the sign of the infinity (i.e. +infinity or -infinity) will be the same as the sign of the "correct" result). One useful way of thinking of these infinity values is that they preserve as much information about the final result as possible (i.e. that it was very large and negative or that it was very large and positive).

For example, both e^1000000 and 10²⁰⁰ * 10²⁰⁰ result in +infinity as both results are positive yet too large to be represented in either single (32-bit) or double (64-bit) IEEE floating point. On the other hand, 10²⁰⁰ * -10²⁰⁰ would yield -infinity.

Quiet NaNs and Signaling NaNs

There are two types of NaNs - quiet NaNs and signaling NaNs (the abbreviations NaNQ and NaNS are often used for the terms quiet NaN and signaling NaN respectively).

Each of the following operations will result in a quiet NaN:

• any operation having one or more quiet NaNs (or signaling NaNs if the IEEE 754 INVALID exception is disabled) as input values unless the operation has a single defined value if all of the input NaNs are replaced by any possible finite or infinite value²
• real square root of a negative number
• 0.0 * infinity
• 0.0 / 0.0
• infinity / infinity
• REMAINDER(anything,0.0)
• REMAINDER(infinity,anything)
• infinity - infinity (when the signs of the two infinities are the same) or infinity + infinity (when the signs of the two infinities are different)

With the exception of the first case, each of these operations results in a runtime exception if the IEEE 754 INVALID exception is enabled (i.e. the program dies with an ugly geek-readable error message). Operations involving quiet NaNs don't result in exceptions - i.e. they're quiet.

The key result of these rules is that once you get a NaN during a computation, the NaN has a strong tendency to propagate itself throughout the rest of the computation (as essentially any usage of the NaN results in a new NaN).

It can't possibly be emphasized too much that this is a good thing even though it may very well be a very annoying thing! The reason that this is a good thing is that every NaN that you get in your final output represents a value which could not be computed (i.e. if a non-NaN had appeared instead of the NaN then you might have been fooled into believing that the non-NaN was a correct value).

IMPORTANT: a division by zero does NOT result in a NaN unless the numerator is zero or a NaN. Dividing a positive value or +infinity by zero results in +infinity and dividing a negative value or -infinity by zero results in -infinity³. This is, without a doubt, the most common misconception regarding IEEE 754 NaNs.

Note that multiplying a NaN by zero does NOT result in zero but, according to the first rule, results in a NaN.

SIDEBAR: Some processors, like the IBM POWER4, store values into memory faster if the memory location is already in the L1 cache when the store operation occurs. Consequently, some software developers have been known to use the following sequence to clear an array quickly:

DO I = 1, N
    A(I) = A(I) * 0.0
ENDDO

This is a really bad idea as any NaNs in the array before the loop will still be NaNs after the loop as the multiplication of a NaN by 0.0 yields a NaN!

A signaling NaN is never generated by a floating point operation. Consequently, the only way to get a signaling NaN in a program is to either be unlucky (or lucky, depending on your point of view) regarding the value of an uninitialized variable or by explicitly initializing a variable's value to be a signaling NaN. If a signaling NaN is used in a floating point operation and the IEEE 754 INVALID exception is enabled then the operation generates an INVALID exception.

Comparing NaNs

NaNs have one other very important characteristic: every NaN is neither equal to, less than or greater than any other conceivable value (including the NaN itself, an infinity or any other NaN).

For example, if X is a NaN and Y is any conceivable value then the following comparisons are all false:

X equals Y
X > Y
X >= Y
X < Y
X <= Y

On the other hand, if X is a NaN and Y is any conceivable value then the following comparison is true:

X not equals Y

Two possible comparisons are particularily interesting:

Y equals Y
Y not equals Y

The first of these is false if Y is a NaN and true otherwise and the second is true if Y is a NaN and false otherwise. In other words, comparing a value with itself is one way to determine if the value is a NaN.

Note that comparing a value with itself in order to determine if it is a NaN is an unsafe programming practice as an optimizer which doesn't properly take into account IEEE 754 NaNs might eliminate the comparison (since "any value is equal to itself so why bother actually doing the comparison?"). Fortunately, most programming language implementations on systems which support IEEE 754 floating point have a library routine which can be used to determine if a value is a NaN (the C library routine is called isnan).

Performance considerations

Enabling the IEEE 754 INVALID exception (or any of the other IEEE 754 exceptions) can have a DRAMATICALLY negative impact on a program's performance. Consequently, the IEEE 754 standard specifies that all exceptions are to be disabled by default.

If IEEE NaNs and infinities didn't exist then it would be quite difficult to debug a program which does a significant amount of floating point arithmetic without enabling exceptions. Since this could have a VERY negative impact on performance, enabling exceptions for a program which runs for many hours when exceptions are disabled might be totally impractical.

On the other hand, the fact that NaNs (and infinities) have a strong tendency to propagate themselves from where they are created through to where the output is generated makes it considerably easier to debug large floating point intensive programs by simply checking for the presence of NaNs at certain key points. For example, something as simple as summing all of the elements in a matrix will tell you if any of the elements are NaN or infinities (you'll get a NaN if any of the elements are NaNs or if you've got a mixture of positive and negative infinities, and you'll get an infinity if you've got one or more infinities of the same sign (there is a small chance that you'll get an infinity if you've got some VERY large values in the matrix although this is almost certainly a bug anyways)).

Representations of NaNs

The 32-bit IEEE 754 representations of these values are:

Positive infinity: 0x7f800000
Negative infinity: 0xff800000
Signaling NaN: any bit pattern between 0x7f800001 and 0x7fbfffff or any bit pattern between 0xff800001 and 0xffbfffff
Quiet NaN: any bit pattern between 0x7fc00000 and 0x7fffffff or any bit pattern between 0xffc00000 and 0xffffffff

The 64-bit IEEE 754 representations of these values are:

Positive infinity: 0x7ff0000000000000
Negative infinity: 0xfff0000000000000
Signaling NaN: any bit pattern between 0x7ff0000000000001 and 0x7ff7ffffffffffff or any bit pattern between 0xfff0000000000001 and 0xfff7ffffffffffff
Quiet NaN: any bit pattern between 0x7ff8000000000000 and 0x7fffffffffffffff or any bit pattern between 0xfff8000000000000 and 0xffffffffffffffff

Note that there are many different bit patterns which represent NaNs. I've heard that some implementations of the IEEE 754 standard use the extra bits towards the end of the 64-bit NaN representations to encode the location in the program where the NaN was created. This scheme makes it easier for a programmer to debug a program which is generating NaNs by pinpointing the statement that generated the NaN.

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References

• Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic by Professor W. Kahan, 1996 (available on the 'net at http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF (last accessed 2003/03/02))

  Professor William Kahan is essentially the "father" of the IEEE 754 standard. This paper is definitely worth reading if you're interested in IEEE 754 floating point (and how did you get this far if you aren't?).
  
  

• personal experience

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¹The default value is the value that you get if the operation doesn't result in a runtime exception (i.e. if the program doesn't terminate abnormally). Whether or not an operation results in a NaN or a runtime exception depends upon whether the IEEE 754 INVALID exception is disabled or enabled respectively.
²the hypot(x,y) function defined as sqrt(x*x + y*y) yields +infinity if x is infinity regardless of the value of y. Consequently, hypot(infinity,y) should yield +infinity regardless of whether or not y is a NaN.
³this isn't quite true as the IEEE 754 standard has a rather strange concept known as -0 (i.e. negative zero). Dividing a positive finite value by +0 yields +infinity whereas dividing a positive finite value by -0 yields -infinity (similarily negative finite divided by -0 yields +infinity and negative finite divided by +0 yields -infinity).

NaN is a sound, emitted by mathematical equation solving programs such as MatLab or Mathematica. It causes an interesting reaction in some people, usually in math majors or physicists that are forced, by homework or some other form of institutionalized sadism, to rely upon such programs. After three nights work, getting sections of code to run individually, and two weeks of bug fixing, and before all of that a month of theory working, a researcher is understandably on edge. When finally the numbers are poured into the process from the tediously made Excel spreadsheet, the researcher goes and takes a break, gets a bite to eat, sleeps(smoke, if they are a mathematician). Anything that will get her away from that computer screen.

When the researcher finally returns, they will begin scrolling through the data, looking for it but never expecting it. If they were in the room at the time, they'd of heard it, but even if they weren't the sound reverberates through their minds:

¡¡NaN!!

At this point the researcher is crying into his notes(you'll note that this also has the effect of bit flipping the researcher's gender). Weeks of work will have been completely useless for a reason that isn't immediately apparent. The sound reverberates through their soul, even though there is a good chance they don't believe in such a thing. They will feel a deep seated urge to either join the circus or send Stephen Wolfram a pipe bomb. Everything about their research they thought they understood has fallen from focus and the world is nothing but pain.

NaN is the sound that terror makes.

In Mathematica, NaN sounds like a beep.

Nan (?), inerj. [For anan.]

Anan.

[Prov. Eng.]

 

© Webster 1913.