What is the criteria for encoding a mirrored version of a character in Unicode? There seems to be a lot of inconsistencies in currently encoded characters. For eg:
'∼'(U+223C, Tilde operator) is mirrored with '∽'(U+223D, Reversed tilde). But similar looking (why there are two characters for tilde is yet another question by itself :|) '~'(U+007E, Tilde) is not mirrored with anything.
'≃'(U+2243, Asymptotically equal to) is mirrored with '⋍'(U+22CD, Reverse tilde equals). Whereas related '≄'(U+2244, Not asymptotically equal to) and '≈'(U+2248, Almost equal to) are mirrored but don't have dedicated characters.
'≾'(U+227E, Precedes or equivalent to) is wrongly mirrored with '≿'(U+227F, Succeeds or equivalent to), since it's upper half is only mirrored here and the lower half remains unmirrored.
Is there any source from where I can know why a character was encoded in UCS standard? Like many redundant characters have been encoded for legacy compatibility reasons. But there many other which I don't understand, like, if mirror of '≈'(U+2248, Almost equal to) is left to the rendering system while mirror of '≃'(U+2243, Asymptotically equal to) is explicitly encoded. I know Mirror of '<'(U+003C, Less-than sign) is also encoded. But it just so happens to be another different character '>'(U+003E, Greater-than sign), unlike the above case.
Related
I know that UTF-16 is a self-synchronizing encoding scheme. I also read the below Wiki, but did not quite get it.
Self Synchronizing Code
Can you please explain me with an example of UTF-16?
In UTF-16 characters outside of the BMP are represented using a surrogate pair in with the first code unit (CU) lies between 0xD800—0xDBFF and the second one between 0xDC00—0xDFFF. Each of the CU represents 10 bits of the code point. Characters in the BMP is encoded as itself.
Now the synchronization is easy. Given the position of any arbitrary code unit:
If the code unit is in the 0xD800—0xDBFF range, it's the first code unit of two, just read the next one and decode. Voilà, we have a full character outside of BMP
If the code unit is in the 0xDC00—0xDFFF range, it's the second code unit of two, just go back one unit to read the first part, or advance to the next unit to skip the current character
If it's in neither of those ranges then it's a character in BMP. We don't need to do anything more
In UTF-16 CU is the unit, i.e. the smallest element. We work at the CU level and read the CU one-by-one instead of byte-by-byte. Because of that along with historical reasons UTF-16 is only self-synchronizable at CU level.
The point of self-synchronization is to know whether we're in the middle of something immediately instead of having to read again from the start and check. UTF-16 allows us to do that
Since the ranges for the high surrogates, low surrogates, and valid BMP characters are disjoint, it is not possible for a surrogate to match a BMP character, or for (parts of) two adjacent characters to look like a legal surrogate pair. This simplifies searches a great deal. It also means that UTF-16 is self-synchronizing on 16-bit words: whether a code unit starts a character can be determined without examining earlier code units. UTF-8 shares these advantages, but many earlier multi-byte encoding schemes (such as Shift JIS and other Asian multi-byte encodings) did not allow unambiguous searching and could only be synchronized by re-parsing from the start of the string (UTF-16 is not self-synchronizing if one byte is lost or if traversal starts at a random byte).
https://en.wikipedia.org/wiki/UTF-16#Description
Of course that means UTF-16 may be not suitable for working over a medium without error correction/detection like a bare network environment. However in a proper local environment it's a lot better than working without self-synchronization. For example in DOS/V for Japanese every time you press Backspace you must iterate from the start to know which character was deleted because in the awful Shift-JIS encoding there's no way to know how long the character before the cursor is without a length map
As a C++ developer supporting unicode is, putting it mildly, a pain in the butt. Unicode has a few unfortunate properties that makes it very hard to determine the case of a letter, convert them or pretty much anything beyond identifying a single known codepoint or so (which may or may not be a letter). The only real rescue, it seems, is ICU for those who are unfortunate enough to not have unicode support builtin the language (i.e. C and C++). Support for unicode in other languages may or may not be good enough.
So, I thought, there must be a real alternative to unicode! i.e. an encoding that does allow easy identification of character classes, besides having a lookup datastructure (tree, table, whatever), and identifying the relationship between characters? I suspect that any such encoding would likely be multi-byte for most text -- that's not a real concern to me, but I accept that it is for others. Providing such an encoding is a lot of work, so I'm not really expecting any such encoding to exist 😞.
Short answer: not that I know of.
As a non-C++ developer, I don't know what specifically is a pain about Unicode, but since you didn't tag the question with C++, I still dare to attempt an answer.
While I'm personally very happy about Unicode in general, I agree that some aspects are cumbersome.
Some of them could arguably be improved if Unicode was redesigned from scratch, eg. by removing some redundancies like the "Latin Greek" math letters besides the actual Greek ones (but that would also break compatibility with older encodings).
But most of the "pains" just reflect the chaotic usage of writing in the first place.
You mention yourself the problem of uppercase "i", which is "I" in some, "İ" in other orthographies, but there are tons of other difficulties – eg. German "ß", which is lowercase, but has no uppercase equivalent (well, it has now, but is rarely used); or letters that look different in final position (Greek "σ"/"ς"); or quotes with inverted meaning («French style» vs. »Swiss style«, “English” vs. „German style“)... I could continue for a while.
I don't see how an encoding could help with that, other than providing tables of character properties, equivalences, and relations, which is what Unicode does.
You say in comments that, by looking at the bytes of an encoded character, you want it to tell you if it's upper or lower case.
To me, this sounds like saying: "When I look at a number, I want it to tell me if it's prime."
I mean, not even ASCII codes tell you if they are upper or lower case, you just memorised the properties table which tells you that 41..5A is upper, 61..7A is lower case.
But it's hard to memorise or hardcode these ranges for all 120k Unicode codepoints. So the easiest thing is to use a table look-up.
There's also a bit of confusion about what "encoding" means.
Unicode doesn't define any byte representation, it only assigns codepoints, ie. integers, to character definitions, and it maintains the said tables.
Encodings in the strict sense ("codecs") are the transformation formats (UTF-8 etc.), which define a mapping between the codepoints and their byte representation.
Now it would be possible to define a new UTF which maps codepoints to bytes in a way that provides a pattern for upper/lower case.
But what could that be?
Odd for upper, even for lower case?
But what about letters without upper-/lower-case distinction?
And then, characters that aren't letters?
And what about all the other character categories – punctuation, digits, whitespace, symbols, combining diacritics –, why not represent those as well?
You could put each in a predefined range, but what happens if too many new characters are added to one of the categories?
To sum it up: I don't think what you ask for is possible.
This is actually related to code golf in general, but also appliable elsewhere. People commonly use base64 encoding to store large amounts of binary data in source code.
Assuming all programming languages to be happy to read Unicode source code, what is the max N, for which we can reliably devise a baseN encoding?
Reliability here means being able to encode/decode any data, so every single combination of input bytes can be encoded, and then decoded. The encoded form is free from this rule.
The main goal is to minimize the character count, regardless of byte-count.
Would it be base2147483647 (32-bit) ?
Also, because I know it may vary from browser-to-browser, and we already have problems with copy-pasting code from codegolf answers to our editors, the copy-paste-ability is also a factor here. I know there is a Unicode range of characters that are not displayed.
NOTE:
I know that for binary data, base64 usually expands data, but here the character-count is the main factor.
It really depends on how reliable you want the encoding to be. Character encodings are designed with trade-offs, and in general the more characters allowed, the less likely it is to be universally accepted i.e. less reliable. Base64 isn't immune to this. RFC 3548, published in 2003, mentions that case sensitivity may be an issue, and that the characters + and / may be problematic in certain scenarios. It describes Base32 (no lowercase) and Base16 (hex digits) as potentially safer alternatives.
It does not get better with Unicode. Adding that many characters introduces many more possible points of failure. Depending on how stringent your requirements are, you might have different values for N. I'll cover a few possibilities from large N to small N, adding a requirement each time.
1,114,112: Code points. This is the number of possible code points defined by the Unicode Standard.
1,112,064: Valid UTF. This excludes the surrogates which cannot stand on their own.
1,111,998: Valid for exchange between processes. Unicode reserves 66 code points as permanent non-characters for internal use only. Theoretically, this is the maximum N you could justifiably expect for your copy-paste scenario, but as you noted, in practice many other Unicode strings will fail that exercise.
120,503: Printable characters only, depending on your definition. I've defined it to be all characters outside of the Other and Separator general categories. Also, starting from this bullet point, N is subject to change in future versions of Unicode.
103,595: NFKD normalized Unicode. Unfortunately, many processes automatically normalize Unicode input to a standardized form. If the process used NFKC or NFKD, some information may have been lost. For more reliability, the encoding should thus define a normalization form, with NFKD being better for increasing character count
101,684: No combining characters. These are "characters" which shouldn't stand on their own, such as accents, and are meant to be combined with another base character. Some processes might panic if they are left standing alone, or if there are too many combining characters on a single base character. I've now excluded the Mark category.
85: ASCII85, aka. I want my ASCII back. Okay, this is no longer Unicode, but I felt like mentioning it because it's a lesser known ASCII-only encoding. It's mainly used in Adobe's PostScript and PDF formats, and has a 5:4 encoded data size increase, rather than Base64's 4:3 ratio.
I was reading a few questions on SO about Unicode and there were some comments I didn't fully understand, like this one:
Dean Harding: UTF-8 is a
variable-length encoding, which is
more complex to process than a
fixed-length encoding. Also, see my
comments on Gumbo's answer: basically,
combining characters exist in all
encodings (UTF-8, UTF-16 & UTF-32) and
they require special handling. You can
use the same special handling that you
use for combining characters to also
handle surrogate pairs in UTF-16, so
for the most part you can ignore
surrogates and treat UTF-16 just like
a fixed encoding.
I've a little confused by the last part ("for the most part"). If UTF-16 is treated as fixed 16-bit encoding, what issues could this cause? What are the chances that there are characters outside of the BMP? If there are, what issues could this cause if you'd assumed two-byte characters?
I read the Wikipedia info on Surrogates but it didn't really make things any clearer to me!
Edit: I guess what I really mean is "Why would anyone suggest treating UTF-16 as fixed encoding when it seems bogus?"
Edit2:
I found another comment in "Is there any reason to prefer UTF-16 over UTF-8?" which I think explains this a little better:
Andrew Russell: For performance:
UTF-8 is much harder to decode than
UTF-16. In UTF-16 characters are
either a Basic Multilingual Plane
character (2 bytes) or a Surrogate
Pair (4 bytes). UTF-8 characters can
be anywhere between 1 and 4 bytes
This suggests the point being made was that UTF-16 would not have any three-byte characters, so by assuming 16bits, you wouldn't "totally screw up" by ending up one-byte off. But I'm still not convinced this is any different to assuming UTF-8 is single-byte characters!
UTF-16 includes all "base plane" characters. The BMP covers most of the current writing systems, and includes many older characters that one can practically encounter. Take a look at them and decide whether you really are going to encounter any characters from the extended planes: cuneiform, alchemical symbols, etc. Few people will really miss them.
If you still encounter characters that require extended planes, these are encoded by two code points (surrogates), and you'll see two empty squares or question marks instead of such a non-character. UTF is self-synchronizing, so a part of a surrogate character never looks like a legitimate character. This allows things like string searches to work even if surrogates are present and you don't handle them.
Thus issues arising from treating UTF-16 as effectively USC-2 are minimal, aside from the fact that you don't handle the extended characters.
EDIT: Unicode uses 'combining marks' that render at the space of previous character, like accents, tilde, circumflex, etc. Sometimes a combination of a diacritic mark with a letter can be represented as a distinct code point, e.g. á can be represented as a single \u00e1 instead of a plain 'a' + accent which are \u0061\u0301. Still you can't represent unusual combinations like z̃ as one code point. This makes search and splitting algorithms a bit more complex. If you somehow make your string data uniform (e.g. only using plain letters and combining marks), search and splitting become simple again, but anyway you lose the 'one position is one character' property. A symmetrical problem happens if you're seriously into typesetting and want to explicitly store ligatures like fi or ffl where one code point corresponds to 2 or 3 characters. This is not a UTF issue, it's an issue of Unicode in general, AFAICT.
It is important to understand that even UTF-32 is fixed-length when it comes to code points, not characters. There are many characters that are composed from multiple code points, and therefore you can't really have a Unicode encoding where one number (code unit) corresponds to one character (as perceived by users).
To answer your question - the most obvious issue with treating UTF-16 as fixed-length encoding form would be to break a string in a middle of a surrogate pair so you get two invalid code points. It all really depends what you are doing with the text.
I guess what I really mean is
"Why would anyone suggest treating
UTF-16 as fixed encoding when it seems
bogus?"
Two words: Backwards compatibility.
Unicode was originally intended to use a fixed-width 16-bit encoding (UCS-2), which is why early adopters of Unicode (e.g., Sun with Java and Microsoft with Windows NT), used a 16-bit character type. When it turned out that 65,536 characters wasn't enough for everyone, UTF-16 was developed in order to allow this 16-bit character systems to represent the 16 new "planes".
This meant that characters were no longer fixed-width, so people created the rationalization that "that's OK because UTF-16 is almost fixed width."
But I'm still not convinced this is
any different to assuming UTF-8 is
single-byte characters!
Strictly speaking, it's not any different. You'll get incorrect results for things like "\uD801\uDC00".lower().
However, assuming UTF-16 is fixed width is less likely to break than assuming UTF-8 is fixed-width. Non-ASCII characters are very common in languages other than English, but non-BMP characters are very rare.
You can use the same special handling
that you use for combining characters
to also handle surrogate pairs in
UTF-16
I don't know what he's talking about. Combining sequences, whose constituent characters have an individual identity, are nothing at all like surrogate characters, which are only meaningful in pairs.
In particular, the characters within a combining sequence can be converted to a different encoding form one characters at a time.
>>> 'a'.encode('UTF-8') + '\u0301'.encode('UTF-8')
b'a\xcc\x81'
But not surrogates:
>>> '\uD801'.encode('UTF-8') + '\uDC00'.encode('UTF-8')
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
UnicodeEncodeError: 'utf-8' codec can't encode character '\ud801' in position 0: surrogates not allowed
UTF-16 is a variable-length encoding. The older UCS-2 is not. If you treat a variable-length encoding like fixed (constant length) you risk introducing error whenever you use "number of 16-bit numbers" to mean "number of characters", since the number of characters might actually be less than the number of 16-bit quantities.
The Unicode standard has changed several times along the way. For example, UCS-2 is not a valid encoding anymore. It has been deprecated for a while now.
As mentioned by user 9000, even in UTF-32, you have sequences of characters that are interdependent. The à is a good example, although this character can be canonicalized to \x00E1. So you can make it simple.
Unicode, even when using the UTF-32 encoding, supports up to 30 code points, one after the other, to represent the most complex characters. (The existing characters do not use that many, I think the longest in existence is currently 17 if I'm correct.)
For that reason, Unicode developed Normalization Forms. It actually considers five different forms:
Unnormalized -- a sequence you create manually, for example; text editors are expected to save properly normalized (NFC) code sequences
NFD -- Normalization Form Decomposition
NFKD -- Normalization Form Compatibility Decomposition
NFC -- Normalization Form Canonical Composition
NFKC -- Normalization Form Compatibility Canonical Composition
Although in most situations it does not matter much because long compositions are rare, even in languages that use them.
And in most cases, your code already deals with canonical compositions. However, if you create strings manually in your code, you are not unlikely to create an unnormalized string (assuming you use such long forms).
Properly implemented servers on the Internet are expected to refused strings that are not canonical compositions as per Unicode. Long forms are also forbidden over connections. For example, the UTF-8 encoding technically allows for ASCII characters to be encoded using 1, 2, 3, or 4 bytes (and the old encoding allowed up to 6 bytes!) but those encoding are not permitted.
Any comment on the Internet that contradicts the Unicode Normalization Form document is simply incorrect.
Trying to rephrase: Can you map every combining character combination into one code point?
I'm new to Unicode, but it seems to me that there is no encoding, normalization or representation where one character would be one code point in every case in Unicode. Is this correct?
Is this true for Basic Multilingual Plane also?
If you mean one char == one number (ie: where every char is represented by the same number of bytes/words/what-have-you): in UCS-4, each character is represented by a 4-byte number. That's way more than big enough for every character to be represented by a single value, but it's quite wasteful if you don't need any of the higher chars.
If you mean the compatibility sequences (ie: where e + ´ => é): there are single-character representations for most of the combinations in use in existing modern languages. If you're making up your own language, you could run into problems...but if you're sticking to the ones that people actually use, you'll be fine.
Can you map every combining character
combination into one code point?
Every combining character combination? How would your proposed encoding represent the string "à̴̵̶̷̸̡̢̧̨̛̖̗̘̙̜̝̞̟̠̣̤̥̦̩̪̫̬̭̮̯̰̱̲̳̹̺̻̼͇͈͉͍͎́̂̃̄̅̆̇̈̉̊̋̌̍̎̏̐̑̒̓̔̽̾̿̀́͂̓̈́͆͊͋͌̕̚ͅ͏͓͔͕͖͙͚͐͑͒͗͛ͣͤͥͦͧͨͩͪͫͬͭͮͯ͘͜͟͢͝͞͠͡"? (an 'a' with more than a hundred combining marks attached to it?) It's just not practical.
There are, however, a lot of "precomposed" characters in Unicode, like áçñü. Normalization form C will use these instead of the decomposed version whenever possible.
it seems to me that there is no encoding, normalization or representation where one character would be one code point in every case in Unicode. Is this correct?
Depends on the meaning of the meaning of the word “character.” Unicode has the concepts of abstract character (definition 7 in chapter 3 of the standard: “A unit of information used for the organization, control, or representation of textual data”) and encoded character (definition 11: “An association (or mapping) between an abstract character and a code point”). So a character never is a code point, but for many code points, there exists an abstract character that maps to the code point, this mapping being called “encoded character.” But (definition 11, paragraph 4): “A single abstract character may also be represented by a sequence of code points”
Is this true for Basic Multilingual Plane also?
There is no conceptual difference related to abstract or encoded characters between the BMP and the other planes. The statement above holds for all subsets of the codespace.
Depending on your application, you have to distinguish between the terms glyph, grapheme cluster, grapheme, abstract character, encoded character, code point, scalar value, code unit and byte. All of these concepts are different, and there is no simple mapping between them. In particular, there is almost never a one-to-one mapping between these entities.