UTF-32 (32- bit Unicode Transformation Format ), sometimes called UCS-4, is a fixed-length encoding used to encode Unicode code points that uses exactly 32 bits (four bytes ) per code point (but a number of leading bits must be zero as there are far fewer than 2 Unicode code points, needing actually only 21 bits). In contrast, all other Unicode transformation formats are variable-length encodings. Each 32-bit value in UTF-32 represents one Unicode code point and is exactly equal to that code point's numerical value.
99-515: The main advantage of UTF-32 is that the Unicode code points are directly indexed. Finding the Nth code point in a sequence of code points is a constant-time operation. In contrast, a variable-length code requires linear-time to count N code points from the start of the string. This makes UTF-32 a simple replacement in code that uses integers that are incremented by one to examine each location in
198-506: A Private Use Area . In either approach, the byte value is encoded in the low eight bits of the output code point. These encodings are needed if invalid UTF-8 is to survive translation to and then back from the UTF-16 used internally by Python, and as Unix filenames can contain invalid UTF-8 it is necessary for this to work. The official name for the encoding is UTF-8 , the spelling used in all Unicode Consortium documents. The hyphen-minus
297-483: A computational hardness assumption to prove the difficulty of several other problems in computational game theory , property testing , and machine learning . The complexity class QP consists of all problems that have quasi-polynomial time algorithms. It can be defined in terms of DTIME as follows. In complexity theory, the unsolved P versus NP problem asks if all problems in NP have polynomial-time algorithms. All
396-529: A constant multiplier , and such a multiplier is irrelevant to big O classification, the standard usage for logarithmic-time algorithms is O ( log n ) {\displaystyle O(\log n)} regardless of the base of the logarithm appearing in the expression of T . Algorithms taking logarithmic time are commonly found in operations on binary trees or when using binary search . An O ( log n ) {\displaystyle O(\log n)} algorithm
495-755: A function of the size of the input. Since this function is generally difficult to compute exactly, and the running time for small inputs is usually not consequential, one commonly focuses on the behavior of the complexity when the input size increases—that is, the asymptotic behavior of the complexity. Therefore, the time complexity is commonly expressed using big O notation , typically O ( n ) {\displaystyle O(n)} , O ( n log n ) {\displaystyle O(n\log n)} , O ( n α ) {\displaystyle O(n^{\alpha })} , O ( 2 n ) {\displaystyle O(2^{n})} , etc., where n
594-450: A string , as was commonly done for ASCII . However, Unicode code points are rarely processed in complete isolation, such as combining character sequences and for emoji. The main disadvantage of UTF-32 is that it is space-inefficient, using four bytes per code point, including 11 bits that are always zero. Characters beyond the BMP are relatively rare in most texts (except, for example, in
693-400: A BOM (a change from Windows 7 Notepad ), bringing it into line with most other text editors. Some system files on Windows 11 require UTF-8 with no requirement for a BOM, and almost all files on macOS and Linux are required to be UTF-8 without a BOM. Programming languages that default to UTF-8 for I/O include Ruby 3.0, R 4.2.2, Raku and Java 18. Although
792-445: A byte stream encoding of its 32-bit code points. This encoding was not satisfactory on performance grounds, among other problems, and the biggest problem was probably that it did not have a clear separation between ASCII and non-ASCII: new UTF-1 tools would be backward compatible with ASCII-encoded text, but UTF-1-encoded text could confuse existing code expecting ASCII (or extended ASCII ), because it could contain continuation bytes in
891-472: A byte with the high bit set cannot be alone; and in a truly random string a byte with a high bit set has only a 1 ⁄ 15 chance of starting a valid UTF-8 character. This has the (possibly unintended) consequence of making it easy to detect if a legacy text encoding is accidentally used instead of UTF-8, making conversion of a system to UTF-8 easier and avoiding the need to require a Byte Order Mark or any other metadata. Since RFC 3629 (November 2003),
990-422: A constant. Linear time is the best possible time complexity in situations where the algorithm has to sequentially read its entire input. Therefore, much research has been invested into discovering algorithms exhibiting linear time or, at least, nearly linear time. This research includes both software and hardware methods. There are several hardware technologies which exploit parallelism to provide this. An example
1089-792: A deterministic Turing machine form the complexity class known as EXP . Sometimes, exponential time is used to refer to algorithms that have T ( n ) = 2 , where the exponent is at most a linear function of n . This gives rise to the complexity class E . An algorithm is said to be factorial time if T(n) is upper bounded by the factorial function n! . Factorial time is a subset of exponential time (EXP) because n ! ≤ n n = 2 n log n = O ( 2 n 1 + ϵ ) {\displaystyle n!\leq n^{n}=2^{n\log n}=O\left(2^{n^{1+\epsilon }}\right)} for all ϵ > 0 {\displaystyle \epsilon >0} . However, it
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#17327978105061188-440: A deterministic machine which is robust in terms of machine model changes. (For example, a change from a single-tape Turing machine to a multi-tape machine can lead to a quadratic speedup, but any algorithm that runs in polynomial time under one model also does so on the other.) Any given abstract machine will have a complexity class corresponding to the problems which can be solved in polynomial time on that machine. An algorithm
1287-629: A future version of Python is planned to store strings as UTF-8 by default. Modern versions of Microsoft Visual Studio use UTF-8 internally. Microsoft's SQL Server 2019 added support for UTF-8, and using it results in a 35% speed increase, and "nearly 50% reduction in storage requirements." Java internally uses Modified UTF-8 (MUTF-8), in which the null character U+0000 uses the two-byte overlong encoding 0xC0 , 0x80 , instead of just 0x00 . Modified UTF-8 strings never contain any actual null bytes but can contain all Unicode code points including U+0000, which allows such strings (with
1386-477: A null byte appended) to be processed by traditional null-terminated string functions. Java reads and writes normal UTF-8 to files and streams, but it uses Modified UTF-8 for object serialization , for the Java Native Interface , and for embedding constant strings in class files . The dex format defined by Dalvik also uses the same modified UTF-8 to represent string values. Tcl also uses
1485-466: A paper dictionary. As a result, the search space within the dictionary decreases as the algorithm gets closer to the target word. An algorithm is said to run in polylogarithmic time if its time T ( n ) {\displaystyle T(n)} is O ( ( log n ) k ) {\displaystyle O{\bigl (}(\log n)^{k}{\bigr )}} for some constant k . Another way to write this
1584-501: A reader start anywhere and immediately detect character boundaries, at the cost of being somewhat less bit-efficient than the previous proposal. It also abandoned the use of biases that prevented overlong encodings . Thompson's design was outlined on September 2, 1992, on a placemat in a New Jersey diner with Rob Pike . In the following days, Pike and Thompson implemented it and updated Plan 9 to use it throughout, and then communicated their success back to X/Open, which accepted it as
1683-606: A row in the above table to encode a code point less than "First code point" (thus using more bytes than necessary) is termed an overlong encoding . These are a security problem because they allow the same code point to be encoded in multiple ways. Overlong encodings (of ../ for example) have been used to bypass security validations in high-profile products including Microsoft's IIS web server and Apache's Tomcat servlet container. Overlong encodings should therefore be considered an error and never decoded. Modified UTF-8 allows an overlong encoding of U+0000 . The chart below gives
1782-488: A term n c {\displaystyle n^{c}} for any c > 1 {\displaystyle c>1} . Algorithms which run in quasilinear time include: In many cases, the O ( n log n ) {\displaystyle O(n\log n)} running time is simply the result of performing a Θ ( log n ) {\displaystyle \Theta (\log n)} operation n times (for
1881-457: Is O ( log k n ) {\displaystyle O(\log ^{k}n)} . For example, matrix chain ordering can be solved in polylogarithmic time on a parallel random-access machine , and a graph can be determined to be planar in a fully dynamic way in O ( log 3 n ) {\displaystyle O(\log ^{3}n)} time per insert/delete operation. An algorithm
1980-517: Is content-addressable memory . This concept of linear time is used in string matching algorithms such as the Boyer–Moore string-search algorithm and Ukkonen's algorithm . An algorithm is said to run in quasilinear time (also referred to as log-linear time ) if T ( n ) = O ( n log k n ) {\displaystyle T(n)=O(n\log ^{k}n)} for some positive constant k ; linearithmic time
2079-422: Is n . Another example was the graph isomorphism problem , which the best known algorithm from 1982 to 2016 solved in 2 O ( n log n ) {\displaystyle 2^{O\left({\sqrt {n\log n}}\right)}} . However, at STOC 2016 a quasi-polynomial time algorithm was presented. It makes a difference whether the algorithm is allowed to be sub-exponential in
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#17327978105062178-480: Is 16 bits) is almost non-existent. On Unix systems, UTF-32 strings are sometimes, but rarely, used internally by applications, due to the type wchar_t being defined as 32-bit. UTF-32 is also forbidden as an HTML character encoding. Python versions up to 3.2 can be compiled to use them instead of UTF-16 ; from version 3.3 onward, Unicode strings are stored in UTF-32 if there is at least 1 non- BMP character in
2277-461: Is a polynomial time algorithm . The following table summarizes some classes of commonly encountered time complexities. In the table, poly( x ) = x , i.e., polynomial in x . formerly-best algorithm for graph isomorphism An algorithm is said to be constant time (also written as O ( 1 ) {\textstyle O(1)} time) if the value of T ( n ) {\textstyle T(n)} (the complexity of
2376-427: Is a synonym for "tractable", "feasible", "efficient", or "fast". Some examples of polynomial-time algorithms: These two concepts are only relevant if the inputs to the algorithms consist of integers. The concept of polynomial time leads to several complexity classes in computational complexity theory. Some important classes defined using polynomial time are the following. P is the smallest time-complexity class on
2475-430: Is an open problem. Other computational problems with quasi-polynomial time solutions but no known polynomial time solution include the planted clique problem in which the goal is to find a large clique in the union of a clique and a random graph . Although quasi-polynomially solvable, it has been conjectured that the planted clique problem has no polynomial time solution; this planted clique conjecture has been used as
2574-497: Is assumed to be UTF-8 to be losslessly transformed to UTF-16 or UTF-32, by translating the 128 possible error bytes to reserved code points, and transforming those code points back to error bytes to output UTF-8. The most common approach is to translate the codes to U+DC80...U+DCFF which are low (trailing) surrogate values and thus "invalid" UTF-16, as used by Python 's PEP 383 (or "surrogateescape") approach. Another encoding called MirBSD OPTU-8/16 converts them to U+EF80...U+EFFF in
2673-467: Is called CESU-8 . If the Unicode byte-order mark U+FEFF is at the start of a UTF-8 file, the first three bytes will be 0xEF , 0xBB , 0xBF . The Unicode Standard neither requires nor recommends the use of the BOM for UTF-8, but warns that it may be encountered at the start of a file trans-coded from another encoding. While ASCII text encoded using UTF-8 is backward compatible with ASCII, this
2772-489: Is clearly superpolynomial, but some algorithms are only very weakly superpolynomial. For example, the Adleman–Pomerance–Rumely primality test runs for n time on n -bit inputs; this grows faster than any polynomial for large enough n , but the input size must become impractically large before it cannot be dominated by a polynomial with small degree. An algorithm that requires superpolynomial time lies outside
2871-434: Is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor . Since an algorithm's running time may vary among different inputs of the same size, one commonly considers
2970-591: Is considered highly efficient, as the ratio of the number of operations to the size of the input decreases and tends to zero when n increases. An algorithm that must access all elements of its input cannot take logarithmic time, as the time taken for reading an input of size n is of the order of n . An example of logarithmic time is given by dictionary search. Consider a dictionary D which contains n entries, sorted in alphabetical order . We suppose that, for 1 ≤ k ≤ n {\displaystyle 1\leq k\leq n} , one may access
3069-436: Is defined to take superpolynomial time if T ( n ) is not bounded above by any polynomial. Using little omega notation , it is ω ( n ) time for all constants c , where n is the input parameter, typically the number of bits in the input. For example, an algorithm that runs for 2 steps on an input of size n requires superpolynomial time (more specifically, exponential time). An algorithm that uses exponential resources
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3168-488: Is derived from Unicode Transformation Format – 8-bit . Almost every webpage is stored in UTF-8. UTF-8 is capable of encoding all 1,112,064 valid Unicode scalar values using a variable-width encoding of one to four one- byte (8-bit) code units. Code points with lower numerical values, which tend to occur more frequently, are encoded using fewer bytes. It was designed for backward compatibility with ASCII :
3267-409: Is dominant for all countries/languages on the internet, is used in most standards, often the only allowed encoding, and is supported by all modern operating systems and programming languages. The International Organization for Standardization (ISO) set out to compose a universal multi-byte character set in 1989. The draft ISO 10646 standard contained a non-required annex called UTF-1 that provided
3366-597: Is done; for this you can use utf8-c8 ". That UTF-8 Clean-8 variant, implemented by Raku, is an encoder/decoder that preserves bytes as is (even illegal UTF-8 sequences) and allows for Normal Form Grapheme synthetics. Version 3 of the Python programming language treats each byte of an invalid UTF-8 bytestream as an error (see also changes with new UTF-8 mode in Python 3.7 ); this gives 128 different possible errors. Extensions have been created to allow any byte sequence that
3465-456: Is either one continuation byte, or ends at the first byte that is disallowed, so E1,A0,20 is a two-byte error followed by a space. This means an error is no more than three bytes long and never contains the start of a valid character, and there are 21,952 different possible errors. Technically this makes UTF-8 no longer a prefix code (you have to read one byte past some errors to figure out they are an error), but searching still works if
3564-423: Is known. Such problems arise in approximation algorithms; a famous example is the directed Steiner tree problem , for which there is a quasi-polynomial time approximation algorithm achieving an approximation factor of O ( log 3 n ) {\displaystyle O(\log ^{3}n)} ( n being the number of vertices), but showing the existence of such a polynomial time algorithm
3663-517: Is marked with U before the character or string literal. C# has a UTF32Encoding which "represents a UTF-32 encoding of Unicode characters". Though technically invalid, the surrogate halves are often encoded and allowed. This allows invalid UTF-16 (such as Windows filenames) to be translated to UTF-32, similar to how the WTF-8 variant of UTF-8 works. Sometimes paired surrogates are encoded instead of non-BMP characters, similar to CESU-8 . Due to
3762-438: Is not a subset of E. An example of an algorithm that runs in factorial time is bogosort , a notoriously inefficient sorting algorithm based on trial and error . Bogosort sorts a list of n items by repeatedly shuffling the list until it is found to be sorted. In the average case, each pass through the bogosort algorithm will examine one of the n ! orderings of the n items. If the items are distinct, only one such ordering
3861-401: Is not generally agreed upon, however the two most widely used are below. A problem is said to be sub-exponential time solvable if it can be solved in running times whose logarithms grow smaller than any given polynomial. More precisely, a problem is in sub-exponential time if for every ε > 0 there exists an algorithm which solves the problem in time O (2 ). The set of all such problems
3960-417: Is not true when Unicode Standard recommendations are ignored and a BOM is added. A BOM can confuse software that isn't prepared for it but can otherwise accept UTF-8, e.g. programming languages that permit non-ASCII bytes in string literals but not at the start of the file. Nevertheless, there was and still is software that always inserts a BOM when writing UTF-8, and refuses to correctly interpret UTF-8 unless
4059-485: Is of great practical importance. An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm, that is, T ( n ) = O ( n ) for some positive constant k . Problems for which a deterministic polynomial-time algorithm exists belong to the complexity class P , which is central in the field of computational complexity theory . Cobham's thesis states that polynomial time
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4158-642: Is represented by a 31-bit value from 0 to 0x7FFFFFFF (the sign bit was unused and zero). In November 2003, Unicode was restricted by RFC 3629 to match the constraints of the UTF-16 encoding: explicitly prohibiting code points greater than U+10FFFF (and also the high and low surrogates U+D800 through U+DFFF). This limited subset defines UTF-32. Although the ISO standard had (as of 1998 in Unicode 2.1) "reserved for private use" 0xE00000 to 0xFFFFFF, and 0x60000000 to 0x7FFFFFFF these areas were removed in later versions. Because
4257-425: Is said to be subquadratic time if T ( n ) = o ( n 2 ) {\displaystyle T(n)=o(n^{2})} . For example, simple, comparison-based sorting algorithms are quadratic (e.g. insertion sort ), but more advanced algorithms can be found that are subquadratic (e.g. shell sort ). No general-purpose sorts run in linear time, but the change from quadratic to sub-quadratic
4356-449: Is said to run in sub-linear time (often spelled sublinear time ) if T ( n ) = o ( n ) {\displaystyle T(n)=o(n)} . In particular this includes algorithms with the time complexities defined above. The specific term sublinear time algorithm commonly refers to randomized algorithms that sample a small fraction of their inputs and process them efficiently to approximately infer properties of
4455-620: Is significantly faster than exponential time . The worst case running time of a quasi-polynomial time algorithm is 2 O ( log c n ) {\displaystyle 2^{O(\log ^{c}n)}} for some fixed c > 0 {\displaystyle c>0} . When c = 1 {\displaystyle c=1} this gives polynomial time, and for c < 1 {\displaystyle c<1} it gives sub-linear time. There are some problems for which we know quasi-polynomial time algorithms, but no polynomial time algorithm
4554-472: Is sorted. Bogosort shares patrimony with the infinite monkey theorem . An algorithm is said to be double exponential time if T ( n ) is upper bounded by 2 , where poly( n ) is some polynomial in n . Such algorithms belong to the complexity class 2-EXPTIME . WTF-8 UTF-8 is a character encoding standard used for electronic communication. Defined by the Unicode Standard, the name
4653-410: Is that 3SAT , the satisfiability problem of Boolean formulas in conjunctive normal form with at most three literals per clause and with n variables, cannot be solved in time 2 . More precisely, the hypothesis is that there is some absolute constant c > 0 such that 3SAT cannot be decided in time 2 by any deterministic Turing machine. With m denoting the number of clauses, ETH is equivalent to
4752-549: Is the case k = 1 {\displaystyle k=1} . Using soft O notation these algorithms are O ~ ( n ) {\displaystyle {\tilde {O}}(n)} . Quasilinear time algorithms are also O ( n 1 + ε ) {\displaystyle O(n^{1+\varepsilon })} for every constant ε > 0 {\displaystyle \varepsilon >0} and thus run faster than any polynomial time algorithm whose time bound includes
4851-588: Is the class of all parameterized problems ( L , k ) {\displaystyle (L,k)} for which there is a computable function f : N → N {\displaystyle f:\mathbb {N} \to \mathbb {N} } with f ∈ o ( k ) {\displaystyle f\in o(k)} and an algorithm that decides L in time 2 f ( k ) ⋅ poly ( n ) {\displaystyle 2^{f(k)}\cdot {\text{poly}}(n)} . The exponential time hypothesis ( ETH )
4950-452: Is the complexity class SUBEXP which can be defined in terms of DTIME as follows. This notion of sub-exponential is non-uniform in terms of ε in the sense that ε is not part of the input and each ε may have its own algorithm for the problem. Some authors define sub-exponential time as running times in 2 o ( n ) {\displaystyle 2^{o(n)}} . This definition allows larger running times than
5049-531: Is the size in units of bits needed to represent the input. Algorithmic complexities are classified according to the type of function appearing in the big O notation. For example, an algorithm with time complexity O ( n ) {\displaystyle O(n)} is a linear time algorithm and an algorithm with time complexity O ( n α ) {\displaystyle O(n^{\alpha })} for some constant α > 0 {\displaystyle \alpha >0}
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#17327978105065148-417: The complexity class P . Cobham's thesis posits that these algorithms are impractical, and in many cases they are. Since the P versus NP problem is unresolved, it is unknown whether NP-complete problems require superpolynomial time. Quasi-polynomial time algorithms are algorithms whose running time exhibits quasi-polynomial growth , a type of behavior that may be slower than polynomial time but yet
5247-485: The floor function . If w = D ( ⌊ n 2 ⌋ ) {\displaystyle w=D\left(\left\lfloor {\frac {n}{2}}\right\rfloor \right)} --that is to say, the word w is exactly in the middle of the dictionary--then we are done. Else, if w < D ( ⌊ n 2 ⌋ ) {\displaystyle w<D\left(\left\lfloor {\frac {n}{2}}\right\rfloor \right)} --i.e., if
5346-524: The k th entry of the dictionary in a constant time. Let D ( k ) {\displaystyle D(k)} denote this k th entry. Under these hypotheses, the test to see if a word w is in the dictionary may be done in logarithmic time: consider D ( ⌊ n 2 ⌋ ) {\displaystyle D\left(\left\lfloor {\frac {n}{2}}\right\rfloor \right)} , where ⌊ ⌋ {\displaystyle \lfloor \;\rfloor } denotes
5445-399: The replacement character "�" (U+FFFD) and continue decoding. Some decoders consider the sequence E1,A0,20 (a truncated 3-byte code followed by a space) as a single error. This is not a good idea as a search for a space character would find the one hidden in the error. Since Unicode 6 (October 2010) the standard (chapter 3) has recommended a "best practice" where the error
5544-407: The worst-case time complexity , which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity , which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed as
5643-482: The Principles and Procedures document of ISO/IEC JTC 1/SC 2 Working Group 2 states that all future assignments of code points will be constrained to the Unicode range, UTF-32 will be able to represent all UCS code points and UTF-32 and UCS-4 are identical. A fixed number of bytes per code point has theoretical advantages, but each of these has problems in reality: The main use of UTF-32 is in internal APIs where
5742-454: The algorithm) is bounded by a value that does not depend on the size of the input. For example, accessing any single element in an array takes constant time as only one operation has to be performed to locate it. In a similar manner, finding the minimal value in an array sorted in ascending order; it is the first element. However, finding the minimal value in an unordered array is not a constant time operation as scanning over each element in
5841-437: The array is needed in order to determine the minimal value. Hence it is a linear time operation, taking O ( n ) {\textstyle O(n)} time. If the number of elements is known in advance and does not change, however, such an algorithm can still be said to run in constant time. Despite the name "constant time", the running time does not have to be independent of the problem size, but an upper bound for
5940-437: The best-known algorithms for NP-complete problems like 3SAT etc. take exponential time. Indeed, it is conjectured for many natural NP-complete problems that they do not have sub-exponential time algorithms. Here "sub-exponential time" is taken to mean the second definition presented below. (On the other hand, many graph problems represented in the natural way by adjacency matrices are solvable in subexponential time simply because
6039-640: The capability for an application to set UTF-8 as the "code page" for the Windows API, removing the need to use UTF-16; and more recently has recommended programmers use UTF-8, and even states "UTF-16 [...] is a unique burden that Windows places on code that targets multiple platforms". The default string primitive in Go , Julia , Rust , Swift (since version 5), and PyPy uses UTF-8 internally in all cases. Python (since version 3.3) uses UTF-8 internally for Python C API extensions and sometimes for strings and
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#17327978105066138-543: The case of texts with some popular emojis), and can typically be ignored for sizing estimates. This makes UTF-32 close to twice the size of UTF-16 . It can be up to four times the size of UTF-8 depending on how many of the characters are in the ASCII subset. The original ISO/IEC 10646 standard defines a 32-bit encoding form called UCS-4 , in which each code point in the Universal Character Set (UCS)
6237-482: The current version of Python requires an option to open() to read/write UTF-8, plans exist to make UTF-8 I/O the default in Python ;3.15. C++23 adopts UTF-8 as the only portable source code file format (surprisingly there was none before). Backwards compatibility is a serious impediment to changing code and APIs using UTF-16 to use UTF-8, but this is happening. As of May 2019 , Microsoft added
6336-426: The data is single code points or glyphs , rather than strings of characters. For instance, in modern text rendering, it is common that the last step is to build a list of structures each containing coordinates (x, y) , attributes, and a single UTF-32 code point identifying the glyph to draw. Often non-Unicode information is stored in the "unused" 11 bits of each word. Use of UTF-32 strings on Windows (where wchar_t
6435-507: The default encoding in XML and HTML (and not just using UTF-8, also declaring it in metadata), "even when all characters are in the ASCII range ... Using non-UTF-8 encodings can have unexpected results". Lots of software has the ability to read/write UTF-8. It may though require the user to change options from the normal settings, or may require a BOM (byte-order mark) as the first character to read
6534-440: The detailed meaning of each byte in a stream encoded in UTF-8. Not all sequences of bytes are valid UTF-8. A UTF-8 decoder should be prepared for: Many of the first UTF-8 decoders would decode these, ignoring incorrect bits. Carefully crafted invalid UTF-8 could make them either skip or create ASCII characters such as NUL , slash, or quotes, leading to security vulnerabilities. It is also common to throw an exception or truncate
6633-451: The early days of Unicode there were no characters greater than U+FFFF and combining characters were rarely used, so the 16-bit encoding was fixed-size. This made processing of text more efficient, though the gains are nowhere as great as novice programmers may imagine. All such advantages were lost as soon as UTF-16 became variable width as well. The code points U+0800 – U+FFFF take 3 bytes in UTF-8 but only 2 in UTF-16. This led to
6732-425: The entire instance. This type of sublinear time algorithm is closely related to property testing and statistics . Other settings where algorithms can run in sublinear time include: An algorithm is said to take linear time , or O ( n ) {\displaystyle O(n)} time, if its time complexity is O ( n ) {\displaystyle O(n)} . Informally, this means that
6831-426: The file. Examples of software supporting UTF-8 include Microsoft Word , Microsoft Excel (2016 and later), Google Drive , LibreOffice and most databases. Software that "defaults" to UTF-8 (meaning it writes it without the user changing settings, and it reads it without a BOM) has become more common since 2010. Windows Notepad , in all currently supported versions of Windows, defaults to writing UTF-8 without
6930-441: The first 128 characters of Unicode, which correspond one-to-one with ASCII, are encoded using a single byte with the same binary value as ASCII, so that a UTF-8-encoded file using only those characters is identical to an ASCII file. Most software designed for any extended ASCII can read and write UTF-8 (including on Microsoft Windows ) and this results in fewer internationalization issues than any alternative text encoding. UTF-8
7029-537: The first character is a BOM (or the file only contains ASCII). For a long time there was considerable argument as to whether it was better to process text in UTF-16 or in UTF-8. The primary advantage of UTF-16 is that the Windows API required it to be used to get access to all Unicode characters (only recently has this been fixed). This caused several libraries such as Qt to also use UTF-16 strings which propagates this requirement to non-Windows platforms. In
7128-403: The first definition of sub-exponential time. An example of such a sub-exponential time algorithm is the best-known classical algorithm for integer factorization, the general number field sieve , which runs in time about 2 O ~ ( n 1 / 3 ) {\displaystyle 2^{{\tilde {O}}(n^{1/3})}} , where the length of the input
7227-637: The high and low surrogates used by UTF-16 ( U+D800 through U+DFFF ) are not legal Unicode values, and their UTF-8 encodings must be treated as an invalid byte sequence. These encodings all start with 0xED followed by 0xA0 or higher. This rule is often ignored as surrogates are allowed in Windows filenames and this means there must be a way to store them in a string. UTF-8 that allows these surrogate halves has been (informally) called WTF-8 , while another variation that also encodes all non-BMP characters as two surrogates (6 bytes instead of 4)
7326-455: The high bit was set. The name File System Safe UCS Transformation Format ( FSS-UTF ) and most of the text of this proposal were later preserved in the final specification. In August 1992, this proposal was circulated by an IBM X/Open representative to interested parties. A modification by Ken Thompson of the Plan 9 operating system group at Bell Labs made it self-synchronizing , letting
7425-418: The hypothesis that k SAT cannot be solved in time 2 for any integer k ≥ 3 . The exponential time hypothesis implies P ≠ NP . An algorithm is said to be exponential time , if T ( n ) is upper bounded by 2 , where poly( n ) is some polynomial in n . More formally, an algorithm is exponential time if T ( n ) is bounded by O (2 ) for some constant k . Problems which admit exponential time algorithms on
7524-527: The idea that text in Chinese and other languages would take more space in UTF-8. However, text is only larger if there are more of these code points than 1-byte ASCII code points, and this rarely happens in the real-world documents due to spaces, newlines, digits, punctuation, English words, and HTML markup. UTF-8 has the advantages of being trivial to retrofit to any system that could handle an extended ASCII , not having byte-order problems, and taking about 1/2
7623-439: The known inapproximability results for the set cover problem. The term sub-exponential time is used to express that the running time of some algorithm may grow faster than any polynomial but is still significantly smaller than an exponential. In this sense, problems that have sub-exponential time algorithms are somewhat more tractable than those that only have exponential algorithms. The precise definition of "sub-exponential"
7722-412: The language to having only UTF-8 strings (with all the other encodings considered legacy and moved out of the standard library to package) following the "UTF-8 Everywhere Manifesto". C++11 has 2 built-in data types that use UTF-32. The char32_t data type stores 1 character in UTF-32. The u32string data type stores a string of UTF-32-encoded characters. A UTF-32-encoded character or string literal
7821-473: The large number of unused 32-bit values, it is also possible to preserve invalid UTF-8 by using non-Unicode values to encode UTF-8 errors, though there is no standard for this. UTF-32 has 2 versions for big-endian and little-endian: UTF-32-BE and UTF-32-LE . Constant time In theoretical computer science , the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm . Time complexity
7920-441: The last byte of a code point to decode it. Unlike many earlier multi-byte text encodings such as Shift-JIS , it is self-synchronizing so searches for short strings or characters are possible and that the start of a code point can be found from a random position by backing up at most 3 bytes. The values chosen for the lead bytes means sorting a list of UTF-8 strings puts them in the same order as sorting UTF-32 strings. Using
8019-655: The notation, see Big O notation § Family of Bachmann–Landau notations ). For example, binary tree sort creates a binary tree by inserting each element of the n -sized array one by one. Since the insert operation on a self-balancing binary search tree takes O ( log n ) {\displaystyle O(\log n)} time, the entire algorithm takes O ( n log n ) {\displaystyle O(n\log n)} time. Comparison sorts require at least Ω ( n log n ) {\displaystyle \Omega (n\log n)} comparisons in
8118-562: The range 0x21–0x7E that meant something else in ASCII, e.g., 0x2F for / , the Unix path directory separator. In July 1992, the X/Open committee XoJIG was looking for a better encoding. Dave Prosser of Unix System Laboratories submitted a proposal for one that had faster implementation characteristics and introduced the improvement that 7-bit ASCII characters would only represent themselves; multi-byte sequences would only include bytes with
8217-494: The remaining 61,440 codepoints of the Basic Multilingual Plane (BMP), including most Chinese, Japanese and Korean characters . Four bytes are needed for the 1,048,576 codepoints in the other planes of Unicode , which include emoji (pictographic symbols), less common CJK characters , various historic scripts, and mathematical symbols . This is a prefix code and it is unnecessary to read past
8316-418: The running time has to be independent of the problem size. For example, the task "exchange the values of a and b if necessary so that a ≤ b {\textstyle a\leq b} " is called constant time even though the time may depend on whether or not it is already true that a ≤ b {\textstyle a\leq b} . However, there is some constant t such that
8415-418: The running time increases at most linearly with the size of the input. More precisely, this means that there is a constant c such that the running time is at most c n {\displaystyle cn} for every input of size n . For example, a procedure that adds up all elements of a list requires time proportional to the length of the list, if the adding time is constant, or, at least, bounded by
8514-590: The same modified UTF-8 as Java for internal representation of Unicode data, but uses strict CESU-8 for external data. All known Modified UTF-8 implementations also treat the surrogate pairs as in CESU-8 . Raku programming language (formerly Perl 6) uses utf-8 encoding by default for I/O ( Perl 5 also supports it); though that choice in Raku also implies "normalization into Unicode NFC (normalization form canonical) . In some cases you may want to ensure no normalization
8613-465: The searched-for string does not contain any errors. Making each byte be an error, in which case E1,A0,20 is two errors followed by a space, also still allows searching for a valid string. This means there are only 128 different errors which makes it practical to store the errors in the output string, or replace them with characters from a legacy encoding. Only a small subset of possible byte strings are error-free UTF-8: several bytes cannot appear;
8712-430: The size of the input is the square of the number of vertices.) This conjecture (for the k-SAT problem) is known as the exponential time hypothesis . Since it is conjectured that NP-complete problems do not have quasi-polynomial time algorithms, some inapproximability results in the field of approximation algorithms make the assumption that NP-complete problems do not have quasi-polynomial time algorithms. For example, see
8811-427: The size of the instance, the number of vertices, or the number of edges. In parameterized complexity , this difference is made explicit by considering pairs ( L , k ) {\displaystyle (L,k)} of decision problems and parameters k . SUBEPT is the class of all parameterized problems that run in time sub-exponential in k and polynomial in the input size n : More precisely, SUBEPT
8910-500: The space for any language using mostly Latin letters. UTF-8 has been the most common encoding for the World Wide Web since 2008. As of November 2024 , UTF-8 is used by 98.4% of surveyed web sites. Although many pages only use ASCII characters to display content, very few websites now declare their encoding to only be ASCII instead of UTF-8. Virtually all countries and languages have 95% or more use of UTF-8 encodings on
9009-643: The specification for FSS-UTF. UTF-8 was first officially presented at the USENIX conference in San Diego , from January 25 to 29, 1993. The Internet Engineering Task Force adopted UTF-8 in its Policy on Character Sets and Languages in RFC ;2277 ( BCP 18) for future internet standards work in January 1998, replacing Single Byte Character Sets such as Latin-1 in older RFCs. In November 2003, UTF-8
9108-645: The string at an error but this turns what would otherwise be harmless errors (i.e. "file not found") into a denial of service , for instance early versions of Python 3.0 would exit immediately if the command line or environment variables contained invalid UTF-8. RFC 3629 states "Implementations of the decoding algorithm MUST protect against decoding invalid sequences." The Unicode Standard requires decoders to: "... treat any ill-formed code unit sequence as an error condition. This guarantees that it will neither interpret nor emit an ill-formed code unit sequence." The standard now recommends replacing each error with
9207-465: The string, but with leading zero bytes optimized away "depending on the [code point] with the largest Unicode ordinal (1, 2, or 4 bytes)" to make all code points that size. Seed7 and Lasso programming languages encode all strings with UTF-32, in the belief that direct indexing is important, whereas the Julia programming language moved away from built-in UTF-32 support with its 1.0 release, simplifying
9306-419: The time required is always at most t . An algorithm is said to take logarithmic time when T ( n ) = O ( log n ) {\displaystyle T(n)=O(\log n)} . Since log a n {\displaystyle \log _{a}n} and log b n {\displaystyle \log _{b}n} are related by
9405-543: The value of the code point. In the following table, the characters u to z are replaced by the bits of the code point, from the positions U+uvwxyz : The first 128 code points (ASCII) need 1 byte. The next 1,920 code points need two bytes to encode, which covers the remainder of almost all Latin-script alphabets , and also IPA extensions , Greek , Cyrillic , Coptic , Armenian , Hebrew , Arabic , Syriac , Thaana and N'Ko alphabets, as well as Combining Diacritical Marks . Three bytes are needed for
9504-594: The web. Many standards only support UTF-8, e.g. JSON exchange requires it (without a byte-order mark (BOM)). UTF-8 is also the recommendation from the WHATWG for HTML and DOM specifications, and stating "UTF-8 encoding is the most appropriate encoding for interchange of Unicode " and the Internet Mail Consortium recommends that all e‑mail programs be able to display and create mail using UTF-8. The World Wide Web Consortium recommends UTF-8 as
9603-418: The word w comes earlier in alphabetical order than the middle word of the whole dictionary--we continue the search in the same way in the left (i.e. earlier) half of the dictionary, and then again repeatedly until the correct word is found. Otherwise, if it comes after the middle word, continue similarly with the right half of the dictionary. This algorithm is similar to the method often used to find an entry in
9702-460: The worst case because log ( n ! ) = Θ ( n log n ) {\displaystyle \log(n!)=\Theta (n\log n)} , by Stirling's approximation . They also frequently arise from the recurrence relation T ( n ) = 2 T ( n 2 ) + O ( n ) {\textstyle T(n)=2T\left({\frac {n}{2}}\right)+O(n)} . An algorithm
9801-413: Was restricted by RFC 3629 to match the constraints of the UTF-16 character encoding: explicitly prohibiting code points corresponding to the high and low surrogate characters removed more than 3% of the three-byte sequences, and ending at U+10FFFF removed more than 48% of the four-byte sequences and all five- and six-byte sequences. UTF-8 encodes code points in one to four bytes, depending on
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