How to compare a "basic_string" using an arbitary locale

Question

I'm re-posting a question I submitted earlier today but I'm now citing a specific example in response to the feedback I received. The original question can be found here (note that it's not a homework assignment):

I'm simply trying to determine if C++ makes it impossible to perform an (efficient) case-INsensitive comparison of a basic_string object that also factors in any arbitrary locale object. For instance, it doesn't appear to be possible to write an efficient function such as the following:

bool AreStringsEqualIgnoreCase(const string &str1, const string &str2, const locale &loc);

Based on my current understanding (but can someone confirm this), this function has to call both ctype::toupper() and collate::compare() for the given locale (extracted as always using use_facet()). However, because collate::compare() in particular requires 4 pointer args, you either need to pass these 4 args for every char you need to compare (after first calling ctype::toupper()), or alternatively, convert both strings to upppercase first and then make a single call to collate::compare().

The 1st approach is obviously inefficient (4 pointers to pass for each char tested), and the 2nd requires you to convert both strings to uppercase in their entirety (requiring allocation of memory and needless copying/converting of both strings to uppercase). Am I correct about this, i.e., it's not possible to do it efficiently (because there's no way around collate::compare()).

Answer 1

One of the little annoyances about trying to deal in a consistent way with all the world's writing systems is that practically nothing you think you know about characters is actually correct. This makes it tricky to do things like "case-insensitive comparison". Indeed, it is tricky to do any form of locale-aware comparison, and case-insensitivity is additionally thorny.

With some constraints, though, it is possible to accomplish. The algorithm needed can be implemented "efficiently" using normal programming practices (and precomputation of some static data), but it cannot be implemented as efficiently as an incorrect algorithm. It is often possible to trade off correctness for speed, but the results are not pleasant. Incorrect but fast locale implementations may appeal to those whose locales are implemented correctly, but are clearly unsatisfactory for the part of the audience whose locales produce unexpected results.

Lexicographical ordering doesn't work for human beings

Most locales (other than the "C" locale) for languages which have case already handle letter case in the manner expected, which is to use case differences only after all other differences have been taken into account. That is, if a list of words are sorted in the locale's collation order, then words in the list which differ only in case are going to be consecutive. Whether the words with upper case come before or after words with lower case is locale-dependent, but there won't be other words in between.

That result cannot be achieved by any single-pass left-to-right character-by-character comparison ("lexicographical ordering"). And most locales have other collation quirks which also don't yield to naïve lexicographical ordering.

Standard C++ collation should be able to deal with all of these issues, if you have appropriate locale definitions. But it cannot be reduced to lexicographical comparison just using a comparison function over pairs of whar_t, and consequently the C++ standard library doesn't provide that interface.

The following is just a few examples of why locale-aware collation is complicated; a longer explanation, with a lot more examples, is found in Unicode Technical Standard 10.

Where do the accents go?

Most romance languages (and also English, when dealing with borrowed words) consider accents over vowels to be a secondary characteristic; that is, words are first sorted as though the accents weren't present, and then a second pass is made in which unaccented letters come before accented letters. A third pass is necessary to deal with case, which is ignored in the first two passes.

But that doesn't work for Northern European languages. The alphabets of Swedish, Norwegian and Danish have three extra vowels, which follow z in the alphabet. In Swedish, these vowels are written å, ä, and ö; in Norwegian and Danish, these letters are written å, æ, and ø, and in Danish å is sometimes written aa, making Aarhus the last entry in an alphabetical list of Danish cities.

In German, the letters ä, ö, and ü are generally alphabetised as with romance accents, but in German phonebooks (and sometimes other alphabetical lists), they are alphabetised as though they were written ae, oe and ue, which is the older style of writing the same phonemes. (There are many pairs of common surnames such as "Müller" and "Mueller" are pronounced the same and are often confused, so it makes sense to intercollate them. A similar convention was used for Scottish names in Canadian phonebooks when I was young; the spellings M', Mc and Mac were all clumped together since they are all phonetically identical.)

One symbol, two letters. Or two letters, one symbol

German also has the symbol ß which is collated as though it were written out as ss, although it is not quite identical phonetically. We'll meet this interesting symbol again a bit later.

In fact, many languages consider digraphs and even trigraphs to be single letters. The 44-letter Hungarian alphabet includes Cs, Dz, Dzs, Gy, Ly, Ny, Sz, Ty, and Zs, as well as a variety of accented vowels. However, the language most commonly referenced in articles about this phenomenon -- Spanish -- stopped treating the digraphs ch and ll as letters in 1994, presumably because it was easier to force Hispanic writers to conform to computer systems than to change the computer systems to deal with Spanish digraphs. (Wikipedia claims it was pressure from "UNESCO and other international organizations"; it took quite a while for everyone to accept the new alphabetization rules, and you still occasionally find "Chile" after "Colombia" in alphabetical lists of South American countries.)

Summary: comparing character strings requires multiple passes, and sometimes requires comparing groups of characters

Making it all case-insensitive

Since locales handle case correctly in comparison, it should not really be necessary to do case-insensitive ordering. It might be useful to do case-insensitive equivalence-class checking ("equality" testing), although that raises the question of what other imprecise equivalence classes might be useful. Unicode normalization, accent deletion, and even transcription to latin are all reasonable in some contexts, and highly annoying in others. But it turns out that case conversions are not as simple as you might think, either.

Because of the existence of di- and trigraphs, some of which have Unicode codepoints, the Unicode standard actually recognizes three cases, not two: lower-case, upper-case and title-case. The last is what you use to upper case the first letter of a word, and it's needed, for example, for the Croatian digraph dž (U+01C6; a single character), whose uppercase is DŽ (U+01C4) and whose title case is Dž (U+01C5). The theory of "case-insensitive" comparison is that we could transform (at least conceptually) any string in such a way that all members of the equivalence class defined by "ignoring case" are transformed to the same byte sequence. Traditionally this is done by "upper-casing" the string, but it turns out that that is not always possible or even correct; the Unicode standard prefers the use of the term "case-folding", as do I.

C++ locales aren't quite up to the job

So, getting back to C++, the sad truth is that C++ locales do not have sufficient information to do accurate case-folding, because C++ locales work on the assumption that case-folding a string consists of nothing more than sequentially and individually upper-casing each codepoint in the string using a function which maps a codepoint to another codepoint. As we'll see, that just doesn't work, and consequently the question of its efficiency is irrelevant. On the other hand, the ICU library has an interface which does case-folding as correctly as the Unicode database allows, and its implementation has been crafted by some pretty good coders so it is probably just about as efficient as possible within the constraints. So I'd definitely recommend using it.

If you want a good overview of the difficulty of case-folding, you should read sections 5.18 and 5.19 of the Unicode standard (PDF for chapter 5). The following is just a few examples.

A case transform is not a mapping from single character to single character

The simplest example is the German ß (U+00DF), which has no upper-case form because it never appears at the beginning of a word, and traditional German orthography didn't use all-caps. The standard upper-case transform is SS (or in some cases SZ) but that transform is not reversible; not all instances of ss are written as ß. Compare, for example, grüßen and küssen (to greet and to kiss, respectively). In v5.1, ẞ, an "upper-case ß, was added to Unicode as U+1E9E, but it is not commonly used except in all-caps street signs, where its use is legally mandated. The normal expectation of upper-casing ß would be the two letters SS.

Not all ideographs (visible characters) are single character codes

Even when a case transform maps a single character to a single character, it may not be able to express that as a wchar→wchar mapping. For example, ǰ can easily be capitalized to J̌, but the former is a single combined glyph (U+01F0), while the second is a capital J with a combining caron (U+030C).

There is a further problem with glyphs like ǰ:

Naive character by character case-folding can denormalize

Suppose we upper-case ǰ as above. How do we capitalize ǰ̠ (which, in case it doesn't render properly on your system, is the same character with an bar underneath, another IPA convention)? That combination is U+01F0,U+0320 (j with caron, combining minus sign below), so we proceed to replace U+01F0 with U+004A,U+030C and then leave the U+0320 as is: J̠̌. That's fine, but it won't compare equal to a normalized capital J with caron and minus sign below, because in the normal form the minus sign diacritic comes first: U+004A,U+0320,U+030C (J̠̌, which should look identical). So sometimes (rarely, to be honest, but sometimes) it is necessary to renormalize.

Leaving aside unicode wierdness, sometimes case-conversion is context-sensitive

Greek has a lot of examples of how marks get shuffled around depending on whether they are word-initial, word-final or word-interior -- you can read more about this in chapter 7 of the Unicode standard -- but a simple and common case is Σ, which has two lower-case versions: σ and ς. Non-greeks with some maths background are probably familiar with σ, but might not be aware that it cannot be used at the end of a word, where you must use ς.

In short

1. The best available correct way to case-fold is to apply the Unicode case-folding algorithm, which requires creating a temporary string for each source string. You could then do a simple bytewise comparison between the two transformed strings in order to verify that the original strings were in the same equivalence class. Doing a collation ordering on the transformed strings, while possible, is rather less efficient than collation ordering the original strings, and for sorting purposes, the untransformed comparison is probably as good or better than the transformed comparison.

2. In theory, if you are only interested in case-folded equality, you could do the transformations linearly, bearing in mind that the transformation is not necessarily context-free and is not a simple character-to-character mapping function. Unfortunately, C++ locales don't provide you the data you need to do this. The Unicode CLDR comes much closer, but it's a complex datastructure.

3. All of this stuff is really complicated, and rife with edge cases. (See the note in the Unicode standard about accented Lithuanian i's, for example.) You're really better off just using a well-maintained existing solution, of which the best example is ICU.