title: Boolean satisfiability problem

text: In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called "satisfiable". On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is "unsatisfiable". For example, the formula ""a" AND NOT "b"" is satisfiable because one can find the values "a" = TRUE and "b" = FALSE, which make ("a" AND NOT "b") = TRUE. In contrast, ""a" AND NOT "a"" is unsatisfiable.


title: Boolean satisfiability problem

text: SAT is the first problem that was proved to be NP-complete; see Cook–Levin theorem. This means that all problems in the complexity class NP, which includes a wide range of natural decision and optimization problems, are at most as difficult to solve as SAT. There is no known algorithm that efficiently solves each SAT problem, and it is generally believed that no such algorithm exists; yet this belief has not been proved mathematically, and resolving the question of whether SAT has a polynomial-time algorithm is equivalent to the P versus NP problem, which is a famous open problem in the theory of computing.


title: Boolean satisfiability problem

text: Nevertheless, as of 2007, heuristic SAT-algorithms are able to solve problem instances involving tens of thousands of variables and formulas consisting of millions of symbols, which is sufficient for many practical SAT problems from, e.g., artificial intelligence, circuit design, and automatic theorem proving.


title: Boolean satisfiability problem

text: A "propositional logic formula", also called "Boolean expression", is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses.


title: Boolean satisfiability problem

text: A formula is said to be "satisfiable" if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to its variables.


title: Boolean satisfiability problem

text: This decision problem is of central importance in many areas of computer science, including theoretical computer science, complexity theory, algorithmics, cryptography and artificial intelligence.


title: Boolean satisfiability problem

text: A "literal" is either a variable (in which case it is called a "positive literal") or the negation of a variable (called a "negative literal").


title: Boolean satisfiability problem

text: A "clause" is a disjunction of literals (or a single literal). A clause is called a "Horn clause" if it contains at most one positive literal.


title: Boolean satisfiability problem

text: A formula is in "conjunctive normal form" (CNF) if it is a conjunction of clauses (or a single clause).


title: Boolean satisfiability problem

text: For example, is a positive literal, is a negative literal, is a clause. The formula is in conjunctive normal form; its first and third clauses are Horn clauses, but its second clause is not. The formula is satisfiable, by choosing "x" = FALSE, "x" = FALSE, and "x" arbitrarily, since (FALSE ∨ ¬FALSE) ∧ (¬FALSE ∨ FALSE ∨ "x") ∧ ¬FALSE evaluates to (FALSE ∨ TRUE) ∧ (TRUE ∨ FALSE ∨ "x") ∧ TRUE, and in turn to TRUE ∧ TRUE ∧ TRUE (i.e. to TRUE). In contrast, the CNF formula "a" ∧ ¬"a", consisting of two clauses of one literal, is unsatisfiable, since for "a"=TRUE or "a"=FALSE it evaluates to TRUE ∧ ¬TRUE (i.e., FALSE) or FALSE ∧ ¬FALSE (i.e., again FALSE), respectively.


title: Boolean satisfiability problem

text: For some versions of the SAT problem, it is useful to define the notion of a "generalized conjunctive normal form" formula, viz. as a conjunction of arbitrarily many "generalized clauses", the latter being of the form for some Boolean function "R" and (ordinary) literals . Different sets of allowed boolean functions lead to different problem versions. As an example, "R"(¬"x","a","b") is a generalized clause, and "R"(¬"x","a","b") ∧ "R"("b","y","c") ∧ "R"("c","d",¬"z") is a generalized conjunctive normal form. This formula is used below, with "R" being the ternary operator that is TRUE just when exactly one of its arguments is.


title: Boolean satisfiability problem

text: Using the laws of Boolean algebra, every propositional logic formula can be transformed into an equivalent conjunctive normal form, which may, however, be exponentially longer. For example, transforming the formula


title: Boolean satisfiability problem

text: while the former is a disjunction of "n" conjunctions of 2 variables, the latter consists of 2 clauses of "n" variables.


title: Boolean satisfiability problem

text: However, with use of the Tseytin transformation, we may find an equisatisfiable conjunctive normal form formula with length linear in the size of the original propositional logic formula.


title: Boolean satisfiability problem

text: SAT was the first known NP-complete problem, as proved by Stephen Cook at the University of Toronto in 1971 and independently by Leonid Levin at the Russian Academy of Sciences in 1973. Until that time, the concept of an NP-complete problem did not even exist.


title: Boolean satisfiability problem

text: The proof shows how every decision problem in the complexity class NP can be reduced to the SAT problem for CNF formulas, sometimes called CNFSAT.


title: Boolean satisfiability problem

text: A useful property of Cook's reduction is that it preserves the number of accepting answers. For example, deciding whether a given graph has a 3-coloring is another problem in NP; if a graph has 17 valid 3-colorings, the SAT formula produced by the Cook–Levin reduction will have 17 satisfying assignments.


title: Boolean satisfiability problem

text: NP-completeness only refers to the run-time of the worst case instances. Many of the instances that occur in practical applications can be solved much more quickly. See Algorithms for solving SAT below.


title: Boolean satisfiability problem

text: Like the satisfiability problem for arbitrary formulas, determining the satisfiability of a formula in conjunctive normal form where each clause is limited to at most three literals is NP-complete also; this problem is called 3-SAT, 3CNFSAT, or 3-satisfiability.


title: Boolean satisfiability problem

text: Although the two formulas are not logically equivalent, they are equisatisfiable. The formula resulting from transforming all clauses is at most 3 times as long as its original, i.e. the length growth is polynomial.


title: Boolean satisfiability problem

text: 3-SAT is one of Karp's 21 NP-complete problems, and it is used as a starting point for proving that other problems are also NP-hard. This is done by polynomial-time reduction from 3-SAT to the other problem. An example of a problem where this method has been used is the clique problem: given a CNF formula consisting of "c" clauses, the corresponding graph consists of a vertex for each literal, and an edge between each two non-contradicting literals from different clauses, cf. picture. The graph has a "c"-clique if and only if the formula is satisfiable.


title: Boolean satisfiability problem

text: There is a simple randomized algorithm due to Schöning (1999) that runs in time (4/3) where "n" is the number of variables in the 3-SAT proposition, and succeeds with high probability to correctly decide 3-SAT.


title: Boolean satisfiability problem

text: The exponential time hypothesis asserts that no algorithm can solve 3-SAT (or indeed "k"-SAT for any ) in time (i.e., fundamentally faster than exponential in "n").


title: Boolean satisfiability problem

text: Selman, Mitchell, and Levesque (1996) give empirical data on the difficulty of randomly generated 3-SAT formulas, depending on their size parameters.


title: Boolean satisfiability problem

text: 3-satisfiability can be generalized to k-satisfiability (k-SAT, also k-CNF-SAT), when formulas in CNF are considered with each clause containing up to "k" literals.


title: Boolean satisfiability problem

text: However, since for any "k" ≥ 3, this problem can neither be easier than 3-SAT nor harder than SAT, and the latter two are NP-complete, so must be k-SAT.


title: Boolean satisfiability problem

text: Some authors restrict k-SAT to CNF formulas with exactly k literals. This doesn't lead to a different complexity class either, as each clause with "j" < "k" literals can be padded with fixed dummy variables to


title: Boolean satisfiability problem

text: After padding all clauses, 2-1 extra clauses have to be appended to ensure that only can lead to a satisfying assignment. Since "k" doesn't depend on the formula length, the extra clauses lead to a constant increase in length. For the same reason, it does not matter whether duplicate literals are allowed in clauses, as in .


title: Boolean satisfiability problem

text: Conjunctive normal form (in particular with 3 literals per clause) is often considered the canonical representation for SAT formulas. As shown above, the general SAT problem reduces to 3-SAT, the problem of determining satisfiability for formulas in this form.


title: Boolean satisfiability problem

text: SAT is trivial if the formulas are restricted to those in disjunctive normal form, that is, they are a disjunction of conjunctions of literals. Such a formula is indeed satisfiable if and only if at least one of its conjunctions is satisfiable, and a conjunction is satisfiable if and only if it does not contain both "x" and NOT "x" for some variable "x". This can be checked in linear time. Furthermore, if they are restricted to being in full disjunctive normal form, in which every variable appears exactly once in every conjunction, they can be checked in constant time (each conjunction represents one satisfying assignment). But it can take exponential time and space to convert a general SAT problem to disjunctive normal form; for an example exchange "∧" and "∨" in the above exponential blow-up example for conjunctive normal forms.


title: Boolean satisfiability problem

text: A variant of the 3-satisfiability problem is the one-in-three 3-SAT (also known variously as 1-in-3-SAT and exactly-1 3-SAT).


title: Boolean satisfiability problem

text: Given a conjunctive normal form with three literals per clause, the problem is to determine whether there exists a truth assignment to the variables so that each clause has "exactly" one TRUE literal (and thus exactly two FALSE literals). In contrast, ordinary 3-SAT requires that every clause has "at least" one TRUE literal.


title: Boolean satisfiability problem

text: Formally, a one-in-three 3-SAT problem is given as a generalized conjunctive normal form with all generalized clauses using a ternary operator "R" that is TRUE just if exactly one of its arguments is. When all literals of a one-in-three 3-SAT formula are positive, the satisfiability problem is called one-in-three positive 3-SAT.


title: Boolean satisfiability problem

text: One-in-three 3-SAT, together with its positive case, is listed as NP-complete problem "LO4" in the standard reference, "Computers and Intractability: A Guide to the Theory of NP-Completeness"


title: Boolean satisfiability problem

text: by Michael R. Garey and David S. Johnson. One-in-three 3-SAT was proved to be NP-complete by Thomas Jerome Schaefer as a special case of Schaefer's dichotomy theorem, which asserts that any problem generalizing Boolean satisfiability in a certain way is either in the class P or is NP-complete.


title: Boolean satisfiability problem

text: Schaefer gives a construction allowing an easy polynomial-time reduction from 3-SAT to one-in-three 3-SAT. Let "("x" or "y" or "z")" be a clause in a 3CNF formula. Add six fresh boolean variables "a", "b", "c", "d", "e", and "f", to be used to simulate this clause and no other.


title: Boolean satisfiability problem

text: Then the formula "R"("x","a","d") ∧ "R"("y","b","d") ∧ "R"("a","b","e") ∧ "R"("c","d","f") ∧ "R"("z","c",FALSE) is satisfiable by some setting of the fresh variables if and only if at least one of "x", "y", or "z" is TRUE, see picture (left). Thus any 3-SAT instance with "m" clauses and "n" variables may be converted into an equisatisfiable one-in-three 3-SAT instance with 5"m" clauses and "n"+6"m" variables.


title: Boolean satisfiability problem

text: Another reduction involves only four fresh variables and three clauses: "R"(¬"x","a","b") ∧ "R"("b","y","c") ∧ R("c","d",¬"z"), see picture (right).


title: Boolean satisfiability problem

text: Given a conjunctive normal form with three literals per clause, the problem is to determine if an assignment to the variables exists such that in no clause all three literals have the same truth value. This problem is NP-complete, too, even if no negation symbols are admitted, by Schaefer's dichotomy theorem.


title: Boolean satisfiability problem

text: A 3-SAT formula is "Linear SAT" ("LSAT") if each clause (viewed as a set of literals) intersects at most one other clause, and, moreover, if two clauses intersect, then they have exactly one literal in common. An LSAT formula can be depicted as a set of disjoint semi-closed intervals on a line. Deciding whether an LSAT formula is satisfiable is NP-complete.


title: Boolean satisfiability problem

text: SAT is easier if the number of literals in a clause is limited to at most 2, in which case the problem is called 2-SAT. This problem can be solved in polynomial time, and in fact is complete for the complexity class NL. If additionally all OR operations in literals are changed to XOR operations, the result is called exclusive-or 2-satisfiability, which is a problem complete for the complexity class SL = L.


title: Boolean satisfiability problem

text: The problem of deciding the satisfiability of a given conjunction of Horn clauses is called Horn-satisfiability, or HORN-SAT.


title: Boolean satisfiability problem

text: It can be solved in polynomial time by a single step of the Unit propagation algorithm, which produces the single minimal model of the set of Horn clauses (w.r.t. the set of literals assigned to TRUE).


title: Boolean satisfiability problem

text: Horn-satisfiability is P-complete. It can be seen as P's version of the Boolean satisfiability problem.


title: Boolean satisfiability problem

text: Horn clauses are of interest because they are able to express implication of one variable from a set of other variables. Indeed, one such clause ¬"x" ∨ ... ∨ ¬"x" ∨ "y" can be rewritten as "x" ∧ ... ∧ "x" → "y", that is, if "x"...,"x" are all TRUE, then "y" needs to be TRUE as well.


title: Boolean satisfiability problem

text: A generalization of the class of Horn formulae is that of renameable-Horn formulae, which is the set of formulae that can be placed in Horn form by replacing some variables with their respective negation.


title: Boolean satisfiability problem

text: For example, ("x" ∨ ¬"x") ∧ (¬"x" ∨ "x" ∨ "x") ∧ ¬"x" is not a Horn formula, but can be renamed to the Horn formula ("x" ∨ ¬"x") ∧ (¬"x" ∨ "x" ∨ ¬"y") ∧ ¬"x" by introducing "y" as negation of "x".


title: Boolean satisfiability problem

text: Checking the existence of such a replacement can be done in linear time; therefore, the satisfiability of such formulae is in P as it can be solved by first performing this replacement and then checking the satisfiability of the resulting Horn formula.


title: Boolean satisfiability problem

text: Another special case is the class of problems where each clause contains XOR (i.e. exclusive or) rather than (plain) OR operators.


title: Boolean satisfiability problem

text: This is in P, since an XOR-SAT formula can also be viewed as a system of linear equations mod 2, and can be solved in cubic time by Gaussian elimination; see the box for an example. This recast is based on the kinship between Boolean algebras and Boolean rings, and the fact that arithmetic modulo two forms a finite field. Since "a" XOR "b" XOR "c" evaluates to TRUE if and only if exactly 1 or 3 members of {"a","b","c"} are TRUE, each solution of the 1-in-3-SAT problem for a given CNF formula is also a solution of the XOR-3-SAT problem, and in turn each solution of XOR-3-SAT is a solution of 3-SAT, cf. picture. As a consequence, for each CNF formula, it is possible to solve the XOR-3-SAT problem defined by the formula, and based on the result infer either that the 3-SAT problem is solvable or that the 1-in-3-SAT problem is unsolvable.


title: Boolean satisfiability problem

text: Provided that the complexity classes P and NP are not equal, neither 2-, nor Horn-, nor XOR-satisfiability is NP-complete, unlike SAT.


title: Boolean satisfiability problem

text: The restrictions above (CNF, 2CNF, 3CNF, Horn, XOR-SAT) bound the considered formulae to be conjunctions of subformulae; each restriction states a specific form for all subformulae: for example, only binary clauses can be subformulae in 2CNF.


title: Boolean satisfiability problem

text: Schaefer's dichotomy theorem states that, for any restriction to Boolean functions that can be used to form these subformulae, the corresponding satisfiability problem is in P or NP-complete. The membership in P of the satisfiability of 2CNF, Horn, and XOR-SAT formulae are special cases of this theorem.


title: Boolean satisfiability problem

text: An extension that has gained significant popularity since 2003 is satisfiability modulo theories (SMT) that can enrich CNF formulas with linear constraints, arrays, all-different constraints, uninterpreted functions, "etc." Such extensions typically remain NP-complete, but very efficient solvers are now available that can handle many such kinds of constraints.


title: Boolean satisfiability problem

text: The satisfiability problem becomes more difficult if both "for all" (∀) and "there exists" (∃) quantifiers are allowed to bind the Boolean variables.


title: Boolean satisfiability problem

text: An example of such an expression would be ; it is valid, since for all values of "x" and "y", an appropriate value of "z" can be found, viz. "z"=TRUE if both "x" and "y" are FALSE, and "z"=FALSE else.


title: Boolean satisfiability problem

text: If only ∀ quantifiers are allowed instead, the so-called tautology problem is obtained, which is co-NP-complete.


title: Boolean satisfiability problem

text: If both quantifiers are allowed, the problem is called the quantified Boolean formula problem (QBF), which can be shown to be PSPACE-complete. It is widely believed that PSPACE-complete problems are strictly harder than any problem in NP, although this has not yet been proved. Using highly parallel "P systems", QBF-SAT problems can be solved in linear time.


title: Boolean satisfiability problem

text: Ordinary SAT asks if there is at least one variable assignment that makes the formula true. A variety of variants deal with the number of such assignments:


title: Boolean satisfiability problem

text: Other generalizations include satisfiability for first- and second-order logic, constraint satisfaction problems, 0-1 integer programming.


title: Boolean satisfiability problem

text: While SAT is a decision problem, the search problem of finding a satisfying assignment reduces to SAT. That is, each algorithm which correctly answers if an instance of SAT is solvable can be used to find a satisfying assignment. First, the question is asked on the given formula Φ. If the answer is "no", the formula is unsatisfiable. Otherwise, the question is asked on the partly instantiated formula Φ{"x"=TRUE}, i.e. Φ with the first variable "x" replaced by TRUE, and simplified accordingly. If the answer is "yes", then "x"=TRUE, otherwise "x"=FALSE. Values of other variables can be found subsequently in the same way. In total, "n"+1 runs of the algorithm are required, where "n" is the number of distinct variables in Φ.


title: Boolean satisfiability problem

text: Since the SAT problem is NP-complete, only algorithms with exponential worst-case complexity are known for it. In spite of this, efficient and scalable algorithms for SAT were developed during the 2000s and have contributed to dramatic advances in our ability to automatically solve problem instances involving tens of thousands of variables and millions of constraints (i.e. clauses). Examples of such problems in electronic design automation (EDA) include formal equivalence checking, model checking, formal verification of pipelined microprocessors, automatic test pattern generation, routing of FPGAs, planning, and scheduling problems, and so on. A SAT-solving engine is also considered to be an essential component in the electronic design automation toolbox.


title: Boolean satisfiability problem

text: Major techniques used by modern SAT solvers include the Davis–Putnam–Logemann–Loveland algorithm (or DPLL), conflict-driven clause learning (CDCL), and stochastic local search algorithms such as WalkSAT. Almost all SAT solvers include time-outs, so they will terminate in reasonable time even if they cannot find a solution.


title: Boolean satisfiability problem

text: Different SAT solvers will find different instances easy or hard, and some excel at proving unsatisfiability, and others at finding solutions. Recent attempts have been made to learn an instance's satisfiability using deep learning techniques.


title: Boolean satisfiability problem

text: SAT solvers are developed and compared in SAT-solving contests. Modern SAT solvers are also having significant impact on the fields of software verification, constraint solving in artificial intelligence, and operations research, among others.


title: Boolean satisfiability problem

text: "This article includes material from a column in the ACM SIGDA e-newsletter by Prof. Karem Sakallah Original text is available here"


title: Subscript and superscript

text: A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps most often used in formulas, mathematical expressions, and specifications of chemical compounds and isotopes, but have many other uses as well.


title: Subscript and superscript

text: In professional typography, subscript and superscript characters are not simply ordinary characters reduced in size; to keep them visually consistent with the rest of the font, typeface designers make them slightly heavier (i.e. medium or bold typography) than a reduced-size character would be. The vertical distance that sub- or superscripted text is moved from the original baseline varies by typeface and by use.


title: Subscript and superscript

text: In typesetting, such types are traditionally called "superior" and "inferior" letters, figures, etc., or just "superiors" and "inferiors". In English, most nontechnical use of superiors is archaic. Superior and inferior figures on the baseline are used for fractions and most other purposes, while lowered inferior figures are needed for chemical and mathematical subscripts.


title: Subscript and superscript

text: A single typeface may contain sub- and superscript glyphs at different positions for different uses. The four most common positions are listed here. Because each position is used in different contexts, not all alphanumerics may be available in all positions. For example, subscript letters on the baseline are quite rare, and many typefaces provide only a limited number of superscripted letters. Despite these differences, all reduced-size glyphs go by the same generic terms "subscript" and "superscript", which are synonymous with the terms "inferior letter" (or "number") and "superior letter" (or "number"), respectively. Most fonts that contain superscript/subscript will have predetermined size and orientation that is dependent on the design of the font.


title: Subscript and superscript

text: Perhaps the most familiar example of subscripts is in chemical formulas. For example, the chemical formula for glucose is CHO (meaning that it is a molecule with 6 carbon atoms, 12 hydrogen atoms and 6 oxygen atoms). One of the most famous molecules, water, is known almost universally by its chemical formula: HO (meaning that it contains 2 hydrogen atoms and 1 oxygen atom.)


title: Subscript and superscript

text: A subscript is also used to distinguish between different versions of a subatomic particle. Thus electron, muon, and tau neutrinos are denoted and . A particle may be distinguished by multiple subscripts, such as for the triple bottom omega particle.


title: Subscript and superscript

text: Similarly, subscripts are also used frequently in mathematics to define different versions of the same variable: for example, in an equation "x" and "x" might indicate the initial and final value of "x", while "v" and "v" would stand for the velocities of a rocket and an observer. Commonly, variables with a zero in the subscript are referred to as the variable name followed by "nought" (e.g. v would be read, "v-nought").


title: Subscript and superscript

text: Subscripts are often used to refer to members of a mathematical sequence or set or elements of a vector. For example, in the sequence "O" = (45, −2, 800), "O" refers to the third member of sequence "O", which is 800.


title: Subscript and superscript

text: Also in mathematics and computing, a subscript can be used to represent the radix, or base, of a written number, especially where multiple bases are used alongside each other. For example, comparing values in hexadecimal, denary, and octal one might write C = 12 = 14.


title: Subscript and superscript

text: Subscripted numbers dropped below the baseline are also used for the denominators of stacked fractions, like this: .


title: Subscript and superscript

text: The only common use of these subscripts is for the denominators of diagonal fractions, like ½ or the signs for percent %, permille ‰, and basis point ‱. Certain standard abbreviations are also composed as diagonal fractions, such as (care of), (account of), (addressed to the subject), or in Spanish (cada uno/una, "each one").


title: Subscript and superscript

text: These superscripts typically share a baseline with numerator digits, the top of which are aligned with the top of the full-height numerals of the base font; lowercase ascenders may extend above.


title: Subscript and superscript

text: Ordinal indicators are sometimes written as superscripts (, , , , rather than 1st, 2nd, 3rd, 4th), although many English-language style guides recommend against this use. Other languages use a similar convention, such as 1 or 2 in French, or 4ª and 4º in Galician and Italian, or 4.ª and 4.º in Portuguese and Spanish.


title: Subscript and superscript

text: In medieval manuscripts, many superscript as well as subscript signs were used to abbreviate text. From these developed modern diacritical marks (glyphs, or "accents" placed above or below the letter). Also, in early Middle High German, umlauts and other modifications to pronunciation would be indicated by superscript letters placed directly above the letter they modified. Thus the modern umlaut ü was written as uͤ. Both vowels and consonants were used in this way, as in ſheͨzze and boͮsen. In modern typefaces, these letters are usually smaller than other superscripts, and their baseline is slightly above the base font's midline, making them extend no higher than a typical ordinal indicator.


title: Subscript and superscript

text: Superscripts are used for the standard abbreviations for service mark (℠) and trademark (™). The signs for copyright © and registered trademark ® are also sometimes superscripted, depending on the typeface or house style.


title: Subscript and superscript

text: On handwritten documents and signs, a monetary amount may be written with the cents value superscripted, as in $ or . Often the superscripted numbers are underlined: $, ⁵⁰. The currency symbol itself may also be superscripted, as in .


title: Subscript and superscript

text: Both low and high superscripts can be used to indicate the presence of a footnote in a document, like this or this. Any combination of characters can be used for this purpose; in technical writing footnotes are sometimes composed of letters and numbers together, like this. The choice of low or high alignment depends on taste, but high-set footnotes tend to be more common, as they stand out more from the text.


title: Subscript and superscript

text: In mathematics, high superscripts are used for exponentiation to indicate that one number or variable is raised to the power of another number or variable. Thus "y" is "y" raised to the fourth power, 2 is 2 raised to the power of "x", and the famous equation includes a term for the speed of light squared. This led over time to an "abuse of notation" whereby superscripts indicate iterative function composition, including derivatives. In an unrelated use, superscripts also indicate contravariant tensors in Ricci calculus.


title: Subscript and superscript

text: The charges of ions and subatomic particles are also denoted by superscripts. is a negatively charged chlorine atom, is an atom of lead with a positive charge of four, is an electron, is a positron, and is an antimuon.


title: Subscript and superscript

text: Atomic isotopes are written using superscripts. In symbolic form, the number of nucleons is denoted as a superscripted prefix to the chemical symbol (for example , , , , and ). The letters "m" or "f" may follow the number to indicate metastable or fission isomers, as in or .


title: Subscript and superscript

text: Subscripts and superscripts can also be used together to give more specific information about nuclides. For example, denotes an atom of uranium with 235 nucleons, 92 of which are protons. A chemical symbol can be completely surrounded: is a divalent cation of carbon with 14 nucleons, of which six are protons and 8 are neutrons, and there are two atoms in this chemical compound.


title: Subscript and superscript

text: The numerators of stacked fractions (such as ) usually use high-set superscripts, although some specially designed glyphs keep the top of the numerator aligned with the top of the full-height numerals.


title: Subscript and superscript

text: This image shows the four common locations for subscripts and superscripts, according to their typical uses. The typeface is Minion Pro, set in Adobe Illustrator. Note that the default superscripting algorithms of most word processors would set the "th" and "lle" too high, and the weight of all the subscript and superscript glyphs would be too light.


title: Subscript and superscript

text: Another minor adjustment that is often omitted by renderers is the control of the direction of movement for superscripts and subscripts, when they do not lie on the baseline. Ideally this should allow for the font, e.g. italics are slanting; most renderers adjust the position only vertically and do not also shift it horizontally. This may create a collision with surrounding letters in the same italic font size. One can see an example of such collision on the right side when rendered in HTML (see the figure on the right). To avoid this, it is often desirable to insert a small positive horizontal margin (or a thin space) (on the left side of the first superscript character), or a negative margin (or a tiny backspace) before a subscript. It is more critical with glyphs from fonts in Oblique styles that are more slanted than those from fonts in Italic style, and some fonts reverse the direction of slanting, so there is no general solution except when the renderer takes into account the font metrics properties that specifies the angle of slanting,


title: Subscript and superscript

text: However the same problem occurs more generally between spans of normal glyphs (non-superscript and non-subscript) when slanting styles are mixed.


title: Subscript and superscript

text: Many text editing and word processing programs have automatic subscripting and superscripting features, although these programs usually simply use ordinary characters reduced in size and moved up or downrather than separately designed subscript or superscript glyphs. Professional typesetting programs such as QuarkXPress or Adobe InDesign also have similar features for automatically converting regular type to subscript or superscript. These programs, however, may also offer native OpenType support for the special subscript and superscript glyphs included in many professional typeface packages (such as those shown in the image above).


title: Subscript and superscript

text: In HTML and Wiki syntax, subscript text is produced by putting it inside the tags codice_1 and codice_2. Similarly, superscripts are produced with codice_3. The exact size and position of the resulting characters will vary by font and browser, but are usually reduced to around 75% original size. Note that superscripts are usually placed too high for many typographic purposes.


title: Subscript and superscript

text: In TeX's mathematics mode (as used in MediaWiki), subscripts are typeset with the underscore, while superscripts are made with the caret. Thus codice_4 produces formula_1, and codice_5 produces formula_2.


title: Subscript and superscript

text: In LaTeX text mode the math method above is inappropriate, as letters will be in math italic, so the command codice_6 will give n and codice_7 will give A (textual "sub"scripts are rare, so codice_8 is not built-in, but requires the "fixltx2e" package). As in other systems, when using UTF-8 encoding, the masculine º and feminine ª ordinal indicators can be used as characters, with no need to use a command.


title: Subscript and superscript

text: In line with its origin as a superscript circle, the degree symbol (°) is composed by a superscript circle operator (∘). codice_9.


title: Subscript and superscript

text: Superscripts and subscripts of arbitrary height can be done with the codice_10 command: the first argument is the amount to raise, and the second is the text; a negative first argument will lower the text. In this case the text is not resized automatically, so a sizing command can be included, e.g. codice_11.


title: Subscript and superscript

text: Unicode defines subscript and superscript characters in several areas; in particular, it has a full set of superscript and subscript digits. Owing to the popularity of using these characters to make fractions, most modern fonts render most or all of these as cap height superscripts and baseline subscripts. The same font may align letters and numbers in different ways. Other than numbers, the set of super- and subscript letters and other symbols is incomplete and somewhat random, and many fonts do not contain them. Because of these inconsistencies, these glyphs may not be suitable for some purposes (see "Uses", above).


title: Subscript and superscript

text: Several advanced features of OpenType typefaces are supported for professionally designed subscript and superscript glyphs. Exactly which glyphs are included varies by typeface; some have only basic support for numerals, while others contain a full set of letters, numerals, and punctuation. They can be available via activating codice_12 or codice_13 feature tag. These feature tags can be turned on if software environment support optional features. In addition, some other typefaces placed them in a Unicode Private Use Area.


title: .454 Casull

text: The .454 Casull () is a firearm cartridge, developed as a wildcat cartridge in 1958 by Dick Casull, Duane Marsh and Jack Fullmer. It was announced in November 1959 by "Guns & Ammo" magazine. The design is a lengthened and structurally improved .45 Colt case. The wildcat cartridge went mainstream when Freedom Arms brought a single action five-shot revolver chambered in .454 Casull to the retail firearms market in 1983. Ruger followed in 1997, chambering its Super Redhawk in this caliber. Taurus followed with the Raging Bull model in 1998 and the Taurus Raging Judge Magnum in 2010.


title: .454 Casull

text: The .45 Schofield and .45 Colt cartridges can fit into the .454's chambers, but not the other way around because of the lengthened case (very similar to the relationship between .38 Special and .357 Magnum cartridges, as well as the .44 Special and .44 Magnum cartridges).


title: .454 Casull

text: The .454 Casull was finally commercialized in 1997, when SAAMI published its first standards for the cartridge. The new Casull round uses a small rifle primer rather than a pistol primer, because it develops extremely high chamber pressures of over 60,000 CUP (copper units of pressure) (410 MPa), and the rifle primer has a significantly stronger CUP than a pistol primer.


title: .454 Casull

text: The round is one of the most powerful handgun cartridges in production. The .454 Casull generates almost 5 times the recoil of the .45 Colt, and about 75% more recoil energy than the .44 Magnum. It can deliver a 250 grain (16 g) bullet with a muzzle velocity of over 1,900 feet per second (580 m/s), developing up to 2,000 ft-lb (2.7 kJ) of energy from a handgun. One Buffalo Bore loading drives a heavier, 300 grain, JFN bullet at 1,650 ft/s for 1,813 ft-lb of muzzle energy. The .454 Casull round is primarily intended for hunting medium or large game, metallic silhouette shooting, and bear protection.


title: .454 Casull

text: The Casull cartridges were originally loaded with a triplex load of propellants, which gave progressive burning, aided by the rifle primer ignition, resulting in a progressive acceleration of the bullet as it passed through the barrel.


title: .454 Casull

text: The first commercially available revolver chambered in .454 Casull was made by Freedom Arms in 1983 as a five-shot single action Model 83 revolver that is capable of firing .45 ACP, .45 Colt and .454 Casull with interchangeable cylinders. The .460 Smith & Wesson Magnum cartridge introduced in 2005 is a lengthened .454 Casull cartridge and has the same diameter as a .45 Colt or .454 Casull. Therefore, revolvers chambered for .460 S&W will also chamber .454 Casull, .45 Colt, and .45 Schofield (.45 Smith & Wesson).


title: Cube Entertainment

text: Cube Entertainment Inc. () is a South Korean entertainment company. The company operates as a record label, talent agency, music production company, event management and concert production company, and music publishing house. Cube are known for having "self-composing and self-producing" idols. In April 2020, the founder of Cube, Hong Seung-sung, resigned from the company due to an ownership dispute.


title: Cube Entertainment

text: The label currently manages several artists, namely Jo Kwon, BtoB, Pentagon, Choi Yu-jin, Yoo Seon-ho, (G)I-dle and Lightsum. It also manages several entertainers and actors, including Lee Hwi-jae, Heo Kyung-hwan, Park Mi-sun, Na In-woo, Kim Jin-woo and Park Sun-young.


title: Cube Entertainment

text: It was formerly home to K-pop artists such as 4Minute, Beast, G.NA, Roh Ji-hoon, Hyuna, Rain, E'Dawn, A Train To Autumn, Lai Kuan-lin, Jang Hyun-seung, Elkie, Sorn, Soojin, Yeeun and CLC.


title: Cube Entertainment

text: Cube Entertainment was founded on August 29, 2006, by Hong Seung-sung (aka Simon Hong), former president of JYP Entertainment, and Shin Jung-hwa (Monica Shin) as Playcube Inc. Due to the founder's past relations, Cube is sometimes mistaken as a subsidiary of JYP Entertainment, however, it is an independent corporation.


title: Cube Entertainment

text: In 2009, Cube's first two groups debuted, with girl group 4Minute debuting in June and boy group Beast in October.


title: Cube Entertainment

text: In 2011, independent label A Cube Entertainment was founded, managing girl group Apink, who debuted in April of the same year.


title: Cube Entertainment

text: Comedian Kim Kiri, a regular cast member on Gag Concert, signed onto Cube in September 2012, making him the first comedian under the label.


title: Cube Entertainment

text: During late 2012, Park Chung-min became the CEO of Cube, after founder Hong Seung-sung stepped down due to his sickness.


title: Cube Entertainment

text: In 2013, Korean entertainer Rain signed a contract with Cube Entertainment. He officially joined after he concluded his military service on July 10, 2013. Three months later Cube released a digital single for its new soloist artist, Shin Ji-hoon who placed in the top 6 in Korean singing competition K-pop Star 2. Another new soloist, Oh Ye-ri released her debut digital single, "Because of You" on November 6, 2013. She was the winner of MBC's "MBC College Song Festival" in 2009.


title: Cube Entertainment

text: At the end of 2015, A Cube Entertainment, which manages Huh Gak and Apink, was acquired by its distributor, LOEN Entertainment. LOEN bought 70% shares in A Cube, therefore making it the sole owner of the agency. A Cube became a separate and distinct label under LOEN Entertainment with the new name Plan A Entertainment.


title: Cube Entertainment

text: In February 2016, Cube headquarter located at Cheongdam-dong moved to Seongdong-gu near Seongdong station. In March 2016, Cube acquired Starline Entertainment as subsidiary. In June 2016, Cube's first girl group 4Minute disbanded. In July 2016, Cube Cafe was reopened in the new building called Cafe 20 Space: The Mint Universe. At the end of 2016, Shin Dae-nam was elected to be the new CEO of Cube Entertainment, replacing former CEO Park Chung-min. He was a former editor of the journal Ilgan Sports and president of Yedang Media. New boy group Pentagon debuted in October 2016. This was followed by Cube's third boy group after Beast leaving Cube in December 2016.


title: Cube Entertainment

text: At the beginning of 2017, Universal Music sold their 8% stake in Cube. Following this, Cube Entertainment signed a distribution deal with Kakao M (formerly LOEN) for future music & content circulation. In March, Cube Entertainment reportedly facing a massive deficit after serious operating losses in 2016, the departure of flagship group BEAST, who reportedly made up 45 percent of their total sales and THAAD.


title: Cube Entertainment

text: In mid-2017, Cube's two male trainees Yoo Seon-ho and Lai Kuan-lin participated in Mnet's Produce 101 Season 2. The latter was chosen to be part of the final lineup for project boygroup Wanna One after finishing in 7th place, while Yoo Seon-ho finished in 17th place. Lai Kuan-lin debuted in Wanna One in August 2017, and promoted with the group until December 2018. Meanwhile, Jeon So-yeon, who participated in the first season of Produce 101 and Unpretty Rapstar debuted as a soloist in November 2017 with her song "Jelly". Jo Kwon of ballad group 2AM signed as a solo artist under the label in the same month, after staying for 16 years in JYP Entertainment.


title: Cube Entertainment

text: On November 14, Cube Entertainment released their third quarter earnings, with revenue growth of 15 percent from the second quarter 22 percent, largely due to the success of BtoB, HyunA and the growth of Pentagon and Yoo Seon-ho, video contents and other additional businesses. The same month, D’Live Co., the third-largest cable TV service provider that is seeking to sell its stakes in entertainment units iHQ Inc and Cube Entertainment Inc. Currently, D’Live owns a 45 percent stake in iHQ and a 30 percent in Cube Entertainment.


title: Cube Entertainment

text: TV personality Lee Hwi-jae signed a contract with Cube on March 5, 2018. In a report released in April 2018, Cube said that it had successfully made profit in 2017, a welcome improvement after incurring severe losses in 2016. In April 2018, Yoo Seon-ho debuted as a soloist. On May 2, Cube debuted (G)I-dle, it is their third girl group after 4Minute and CLC. On May 4, Cube Entertainment announced the United Cube Concert – One concert, featuring their own artists. The concert took place at KINTEX in Ilsan on June 16 and was sold out in two minutes.


title: Cube Entertainment

text: On August 2, 2018, photos of Hyuna with Pentagon's E'Dawn at their birthday party on June 4 were released. Cube Entertainment initially denied rumors the two were dating, however Hyuna and E’Dawn held an interview with Yeonhap News later that day, admitting to their relationship which began in May 2016. The company responded to Hyuna's confirmation of the dating rumors by cancelling all previously planned performances for Triple H, on-air appearances, and fan events, including a fan meet-up scheduled for the next day. Fans were divided in reactions to the event, with some calling for E'Dawn to be removed from Pentagon, and others focusing on how the company treated them unfairly after releasing the scandal, rather than on their relationship. On September 13, Cube Entertainment announced that they would be terminating their contracts, citing that they could not "maintain trust" as a reason saying "After much deliberation, we've concluded that the trust between the company and the artists had been damaged to a degree that it cannot be restored, leading us to believe expulsion is necessary," in its official statement. However, Cube declared that the situation is still being considered and nothing has been decided yet for them, saying that the issue will be discussed on a board meeting. A senior official said, “The dismissal of Hyuna and E'Dawn was in discussion but not final. We will have to collect opinions a little more. As the artists' opinions are also important, this is a matter that should be decided carefully through collecting opinions. The departure is not final. Agency officials are having an urgent discussion. As much as possible, we will make decisions based on artists' opinions." On October 15, Cube Entertainment officially confirmed Hyuna's departure, announcing that the record label has reached an agreement with Hyuna to terminate her contract.


title: Cube Entertainment

text: On October 25, Cube signed a contract with Haohao Wenhua Media Company (Hot Idol, Haohao Bangyang Agency) () for activities in China. On November 5, Cube debuted a non-idol ballad group, A Train To Autumn (), with digital single "That Season You Were In". Kino of Pentagon participated as one of the lyricists. On November 14, Cube Entertainment officially confirmed E'Dawn's departure. On November 23, Cube established a new label, U-Cube, with Universal Music Japan for activities in Japan. It was reported that Cube's sales in 2018 increased 46.7% year-on-year to ₩35.8 billion. During the same period, operating profit jumped 809.3% to ₩1.9 billion and net profit turned to profit of ₩1 billion due to the success of BtoB's album sales and concerts, Pentagon's "Shine", (G)I-dle's debut and Lai Guan-lin's activities. Cube's music sales also increased by 58% to ₩8.8 billion due to the popularity of (G)I-dle's "Latata" and "Hann (一)".


title: Cube Entertainment

text: In early 2019, Cube Entertainment chose NetEase Music as its strategic partner as a platform to promote in China. On January 23, D’Live Co. sought to sell its stakes in entertainment units iHQ Inc. and Cube Entertainment Inc. Currently, D’Live owns a 45 percent stake in iHQ and a 30 percent stake in Cube Entertainment. On August 19, Gagman Lee Sang-joon has signed an exclusive contract with Cube. Two days later, it was announced that Produce 48 participant, Han Cho-won and , Lee Joo-hyun were the next to sign. In September, it was reported that Cube Entertainment partnership with e2PR, Strategic Communications for establishing new promotion team for handling (G)I-dle's public international relations. In the fourth quarter of 2019, Cube recorded 22.6 billion won and 40.3 million won in operating profit due to (G)I-dle's "Lion" and Pentagon's Prism World Tour. Overall, Cube's sales in 2019 down 13.9%, operating profit down 51.1% and net profit down 35.8% compared to previous years.


title: Cube Entertainment

text: In early 2020, Comedian Park Mi-sun has signed an exclusive contract with Cube. On February 21, VT GMP reportedly has acquired 30.61% stake in Cube Entertainment, changing Cube's largest shareholder from iHQ to VT GMP, and plans on playing an active role in strengthening the business and pushing the Hallyu Wave through it subsidiary KVLY. On March 26, Shin Dae-nam has resigned as CEO of Cube Entertainment. Ahn Woo-hyung and Lee Dong-kwan was appointed as the new CEO of Cube Entertainment. Ahn Woo-hyung is the CEO of KVLY and Lee Dong-kwan is the VT GMP vice president. On April 17, Cube launched a global fan page U CUBE for fans around the world to communicate with their artists and providing services such as automatic translation in various languages and systems to apply for music show recordings.


title: Cube Entertainment

text: On June 16, 2020, model Moon Su-inn, who debuted as a model in 2014 signed exclusive contract with Cube Entertainment. On June 23, Seongdong-gu district signed an agreement with Cube to promote urban regeneration based on cultural contents through various cultural contents such as festival and YouTube content. On June 25, Cube partnered with VT GMP to launch a new global audition program titled, "See Saw Game" and is expected to air through Chinese streaming platforms. The audition program is developed by SBS' subsidiary Formattist Co., Ltd. and writer Park Won-woo of "King of Mask Singer". On June 2, Cube signed an exclusive contract with Alibaba Group to support the activities of its artists in China. The artists of Cube will receive support from Alibaba for activities such as movies, dramas, advertisements, and performances in China. This is the first time that a Chinese IT company has signed an exclusive contract for artist activities with a Korean agency.


title: Cube Entertainment

text: In September 2020, Cube announced they co-hosted an event called, M.O.M (Message of the Moon) Project. It is a project to deliver messages of hope and wishes in the midst of the outbreak, as well as to launch a large artificial moon with the diameter of 12m and 20m high, and 21 small 2m diameter artificial moons and drive-in cinema at Salgoji Park, Seongdong-gu. On October 21, Cube has signed a strategic business agreement with Hanwha Life Insurance to increase brand awareness, strengthen marketing capabilities and developing new content.


title: Cube Entertainment

text: On December 31, 2020, Cube Entertainment announced that Ilhoon would leave BTOB after being investigated for using marijuana. Ilhoon was under investigation from the Seoul Metropolitan Police Agency for purchasing and using marijuana over the past 4–5 years, and was also charged for violating the Narcotics Control Act.


title: Cube Entertainment

text: On January 6, 2021, Cube Entertainment announced that they had signed a contract with webtoon platform, Comics Family, to produce video content with their IP. The company plans to produce 12 exclusive video content on webtoon IPs per year with Comics Family. They are planning to distribute the dramas globally through various OTT platforms.


title: Cube Entertainment

text: On August 13, 2021, Choi Yu-jin of CLC made an unofficial announcement through "Girls Planet 999" that Cube had told CLC that they would no longer be doing group activities.


title: Cube Entertainment

text: On August 14, 2021, Cube Entertainment announced Soojin's withdrawal from (G)I-dle after a school bullying accusation.


title: Cube Entertainment

text: On October 22, 2021, Choi Yujin of CLC successfully placed 3rd in the final live episode of Mnet's survival show Girls Planet 999, making her debut in the nine-member project group, Kep1er.


title: Cube Entertainment

text: On November 16, 2021, Cube Entertainment announced the departure of Sorn after her exclusive contract got terminated.


title: Cube Entertainment

text: On March 5, 2022, Cube Entertainment announced that Soojin's exclusive contract has been terminated after police investigations concluded that the accusers were not guilty of spreading false information.


title: Cube Entertainment

text: On March 18, 2022, Cube Entertainment announced that Seungyeon and Yeeun would be leaving the company as they had chosen not to renew their contract with the company.


title: Cube Entertainment

text: On May 20, 2022, Cube Entertainment announced that CLC would be disbanding as of June 6 of that year.


title: Cube Entertainment

text: Music Cube（Hangul:뮤직큐브）was founded in Korea on August 18, 2005. It is an independently operated music copyright company that mainly engaged in the publishing, production, visual design and copyright management of music products. The headquarters is located in Nonhyeon-dong, Seoul.


title: Cube Entertainment

text: Music Cube Japan is a Japanese subsidiary of Music Cube. It was founded in Japan on January 21, 2009. It is mainly engaged in the production, development, promotion and copyright management of music products. It is headquartered in Minato, Tokyo.


title: Cube Entertainment

text: Cube DC（Hangul:큐브DC）was founded in 2012. It is a subsidiary of Cube Entertainment. The parent company Cube Entertainment announced on August 27, 2014, that it was acquired as a wholly owned subsidiary.


title: Cube Entertainment

text: Cube Japan（）is an overseas subsidiary of Music Cube. It was founded in Japan in 2012 and is mainly responsible for the overseas promotion and distribution of parent company and related products. The headquarters is located in Minato-ku, Tokyo, and later operated by CUBE Entertainment JAPAN to operate Japanese activities.


title: Cube Entertainment

text: Cube Entertainment Japan (CUBE ENTERTAINMENT JAPAN Co., Ltd.) is a local Japanese company owned by Cube Entertainment. It was founded in Japan on October 27, 2015. It is 100% owned by Cube Entertainment and has a capital of 96 million yen. It is responsible for direct planning and managing activities of the parent company artist in Japan. The headquarters is now located in Aoyama, Minato, Tokyo.


title: Cube Entertainment

text: Starline Entertainment（Hangul: 스타라인엔터테인먼트）On February 12, 2016, Park Sung-soo representatives reached an agreement with Cube Entertainment to become a wholly owned subsidiary of Cube Entertainment.


title: Cube Entertainment

text: Cube TV（Hangul: 큐브TV）was established on July 1, 2015, iHQ cooperates with Cube Entertainment, iHQ investment management channel, Cube provides the program content, is a channel dedicated to promoting K-POP culture, playing variety shows, singing Meeting and online drama. The channel includes BtoB's "Btob Show", CLC's "Seongdong-gu Resident", Pentagon's "Pentagon maker", Triple H's "Triple H Fun Agency ", online drama "Spark" and more.


title: Cube Entertainment

text: Cube TV Hangtime In 2018, Cube Entertainment joined with Kiswe Mobile to created an application of 12 multi-view camera, "Cube TV Hangtime". This is an interactive mobile video which audience can interact with the artist. On June 16, Cube TV Hangtime app aired a four-hour-long of "United Cube Concert – One" for the audience who were unable to attend the concert.


title: Cube Entertainment

text: On November 23, 2018, Cube Music and Universal Music Japan established U-Cube for overseas promotion and distribution of artists and related products.


title: Cube Entertainment

text: Cube Entertainment artists teamed up with US major league team, Los Angeles Dodgers's Korean player Ryu Hyun-jin by donating all the profit from two collaboration songs to Hanbit School for the Blind.


title: Cube Entertainment

text: In September 2015, the artists from the agency performed at the "Cube Festival" concert. The concert was hosted by Shanghai TV, Channel M, and BesTV. At a preceding press conference, a Cube representative said, “A while ago there was a heartbreaking accident in China. BEAST, 4minute, G.Na, BTOB, and CLC donated a portion of their earnings from their recent concert in Shanghai to the victims of the 2015 Tianjin explosions.” Representing the concert organizer, Yeom Gyu Suk from Butterfly Media went on to explain, “While in the midst of preparing for the concert, the event sponsor and Cube Entertainment heard the news of the accident and decided to do the show for the victims, and after gathering the artists agreed.”


title: Cube Entertainment

text: In 2018, Cube Entertainment President Hong Seung-sung joined the Honor Society and gave a donation of more than ₩100 million for patients with rare incurable diseases. Hong Seung-sung, who has been suffering from Lou Gehrig's disease for the past 7 years, said, "As a person suffering from the same pain, I want to be a little push for children with rare diseases that need help." Over the years, it is common for United Cube to participate in the Ice Bucket Challenge, as a way to raise awareness for the disease.


title: Cube Entertainment

text: In April 2019, according to the Disaster Relief Association, Cube Entertainment donated a total of ₩50 Million to the Korean Committee to help those that were affected by the Sokcho Fire. On December 30, Cube delivered ₩10 million through Foundation for International Development Cooperation NGO for a child care facility in Seoul and a promised for monthly donation and volunteer activity.


title: Cube Entertainment

text: On March 6, 2020, Cube and their artists donated 50 million won through Hope Bridge National Disaster Relief Association to prevent the spreading of the COVID-19 pandemic in South Korea. The contribution will be used to support daily necessities, hygiene products and health goods for medical staff and families. In June, Cube Entertainment's parent company, VT GMP donated 10 million won worth of antibacterial paper bags for COVID-19 self-container sanitary kit.


title: Cube Entertainment

text: Cube Entertainment advocates their idols to become artist-type idols through writing, composing, and recording songs. They provide MIDI classes for their trainees and artists.


title: Cube Entertainment

text: On June 17th 2021, the Seoul Central District Court ruled in Lai Kaun-lin's favour and ended his contract with Cube Entertainment. This brought to a close a 2 year dispute that started in July 2019 when Lai requested to terminate his contract. One of the claims Lai made was that Cube Entertainment had sold his artist management rights in China to a third party without notifying him. The judge agreed with Lai and deemed the contract invalid.


title: Cube Entertainment

text: Lai also claimed Cube scheduled conflicting events that he could not attend and impersonated the signature of Lai Kuan-lin's father.


title: Timothy Carlton

text: Carlton was born in Oxford, Oxfordshire, England, the son of Pauline Ellen Laing (née Congdon), who died on 11 October 2007, and Henry Carlton Cumberbatch, a decorated naval officer of both World Wars and a prominent figure of London high society. His grandfather, Henry Arnold Cumberbatch CMG, was the Consul General of Queen Victoria in Turkey.


title: Timothy Carlton

text: He has had a long and distinguished career in both the theatre ("Her Royal Highness" etc.) and in television, appearing in numerous BBC television series over the years since 1966 to the present day, including "Cold Comfort Farm" (1968), the sitcoms "Executive Stress", "Keeping Up Appearances", "Next of Kin" and in the television films "Gauguin the Savage" (1980) and "The Scarlet Pimpernel" (1982). In 2015 he played Donald Sidwell in “Napoleon’s Violin”, S1:E8 of "The Coroner". His film career has included roles in "Baby Love" (1969), "The Breaking of Bumbo" (1970), "That Lucky Touch" (1975), "The Bitch" (1979), "High Road to China" (1983) and "Parting Shots" (1999). He is currently with the theatrical agency Susan Angel and Kevin Francis Ltd. in London.


title: Timothy Carlton

text: Carlton is married to actress Wanda Ventham, whom he met in 1970 while filming sequences for the drama series "A Family At War" and they have been married since April 1976. They appeared together in Series 2 of BBC drama "The Lotus Eaters" in 1973 and Series 3 and 4 of BBC series "Sherlock" in 2014 as the parents of the title character, played by their son, actor Benedict Cumberbatch.


title: BC Ferries

text: British Columbia Ferry Services Inc., operating as BC Ferries (BCF), is a former provincial Crown corporation, now operating as an independently managed, publicly owned Canadian company. BC Ferries provides all major passenger and vehicle ferry services for coastal and island communities in the Canadian province of British Columbia. Set up in 1960 to provide a similar service to that provided by the Black Ball Line and the Canadian Pacific Railway, which were affected by job action at the time, BC Ferries has become the largest passenger ferry line in North America, operating a fleet of 36 vessels with a total passenger and crew capacity of over 27,000, serving 47 locations on the B.C. coast.


title: BC Ferries

text: The federal and provincial governments subsidize BC Ferries to provide agreed service levels on essential links between the BC mainland, coastal islands, and parts of the mainland without road access. The inland ferries operating on British Columbia's rivers and lakes are not run by BC Ferries. The responsibility for their provision rests with the British Columbia Ministry of Transportation, which contracts operation to various private sector companies.


title: BC Ferries

text: At its inception, BC Ferries was a division of the British Columbia Toll Highways and Bridges Authority, a provincial Crown corporation. Through successive reorganizations, it evolved into the British Columbia Ferry Authority and then the British Columbia Ferry Corporation, both of which were also provincial Crown corporations. In 2003, the Government of British Columbia announced that BC Ferries, which had been in debt, would be reorganized into a private corporation, implemented through the passage of the "Coastal Ferry Act" (Bill 18-2003). The single voting share of BC Ferries Corporation is held by the provincial government's BC Ferry Authority, which operates under the rules of the Act.


title: BC Ferries

text: In the summer of 1958, a strike by employees of CP Steamships and the Black Ball Line caused the Social Credit government of W. A. C. Bennett to decide that the coastal ferry service in British Columbia needed to be government-owned, and so it set about creating BC Ferries. Minister of Highways Phil Gaglardi was tasked with overseeing the new Crown corporation and its rapid expansion.


title: BC Ferries

text: BC Ferries' first route, commissioned in 1960, was between Swartz Bay, north of Sidney on Vancouver Island, and Tsawwassen, an area in Delta, using just two vessels. These ships were the now-retired MV "Tsawwassen" and the MV "Sidney". The next few years saw a dramatic growth of the B.C. ferry system as it took over operations of the Black Ball Line and other major private companies providing vehicle ferry service between Vancouver Island and the Lower Mainland. As the ferry system expanded and started to service other small coastal communities, BC Ferries had to build more vessels, many of them in the first five years of its operations, to keep up with the demand. Another method of satisfying increasing demand for service was BC Ferries' unique "stretch and lift" program, involving seven vessels being cut in half and extended, and five of those vessels later cut in half again and elevated, to increase their passenger and vehicle-carrying capacities. The vast majority of the vessels in the fleet were built in B.C. waters, with only two foreign purchases and one domestic purchase. In the mid-1980s, BC Ferries took over the operations of the saltwater branch of the B.C. Ministry of Transportation and Highways, which ran ferry services to very small coastal communities. This action dramatically increased the size of BC Ferries' fleet and its geographical service area. The distinctive "dogwood on green" flag that BC Ferries used between 1960 and 2003 gave the service its popular nickname "the Dogwood Fleet".


title: BC Ferries

text: During the 1990s, the NDP government commissioned a series of three fast ferries to improve ferry service between the Mainland and Vancouver Island. The ships proved problematic when they suffered many technical issues and cost double what was expected. The fast ferries were eventually sold off for $19.4 million in 2003.


title: BC Ferries

text: A controversy began in July 2004 when BC Ferries, under a new American CEO, announced that the company had disqualified all Canadian bids to build three new ships, and only the proposals from European shipyards were being considered. The contract was estimated at $542 million for the three ships, each designed to carry 370 vehicles and 1600 passengers.


title: BC Ferries

text: The argument for domestic construction of the ferries was that it would employ numerous British Columbia workers, revitalize the sagging B.C. shipbuilding industry, and entitle the provincial government to a large portion of the cost in the form of taxes. BC Ferries CEO David Hahn claimed that building the ferries in Germany would "save almost $80 million and could lead to lower fares."


title: BC Ferries

text: On September 17, 2004, BC Ferries awarded the vessel construction contract to Germany's Flensburger shipyard. The contract protected BC Ferries from any delays through a fixed price and fixed schedule contract. entered service in March 2008, while was delivered the same month and entered service in June. The third ship, , has been delivered and is now in service as well.


title: BC Ferries

text: On August 18, 2006, BC Ferries commissioned Flensburger to build a new vessel for its Inside Passage route, with the contract having many of the same types of terms as that for the Coastal-class vessels. The new northern service vessel, , has been delivered.


title: BC Ferries

text: On August 26, 2012, BC Ferries announced that it would be cutting 98 round trips on its major routes starting in the fall and winter of 2012 as part of a four-year plan to save $1 million on these routes. Service cuts have included the elimination of supplementary sailings on the Swartz Bay–Tsawwassen route, 18 round trips on the Horseshoe Bay–Departure Bay route, and 48 round trips, the largest number of cuts, on the Duke Point–Tsawwassen route, with plans to look for savings on the smaller unprofitable routes in the future.


title: BC Ferries

text: In the fall of 2014, BC Ferries announced the addition of three new Intermediate-class ferries to phase out "Queen of Burnaby" and "Queen of Nanaimo". These three vessels were to be named the Salish Class; Salish Orca, Salish Eagle and Salish Raven. In 2022, the Salish Heron, the fourth Salish Class vessel entered service. All four ferries were designed and built by Remontowa Shipbuilding S.A. in Gdansk, Poland, and are dual-fuel, capable of operating on liquefied natural gas and marine diesel. These vessels are a part of BC Ferries standardized fleet plan, which will take the number of ship class in the BC Ferries fleet from 17 to 5. BC Ferries has stated that total standardization of the BC Ferries fleet will not be complete for another 40 years.


title: BC Ferries

text: Route numbers are used internally by BC Ferries. All routes except Route 13 and the Lasqueti Island route allow vehicles.


title: BC Ferries

text: Route 5 – Swanson Channel: Swartz Bay to the Southern Gulf Islands (Galiano, Mayne, Pender, and Saturna Islands)


title: BC Ferries

text: Route 9 – Active Pass Shuttle: Tsawwassen to the Southern Gulf Islands (Galiano, Mayne, Pender and Saltspring Islands)


title: BC Ferries

text: Route 10 Supplemental: servicing Bella Bella, Shearwater, Ocean Falls and Bella Coola (as of mid-2014)


title: BC Ferries

text: Route 13 – Thornbrough Channel: Langdale to Gambier Island (via New Brighton) and Keats Island (via Keats Landing and Eastbourne). (Foot passengers only, no vehicles). (Operated by Kona Winds Yacht Charters Ltd.)


title: BC Ferries

text: Route 25 – Broughton Strait: Port McNeill to Alert Bay (on Cormorant Island) and Sointula (on Malcolm Island)


title: BC Ferries

text: Numbers in blue circles are ferry route numbers. Provincial highway trailblazers are added where appropriate.


title: BC Ferries

text: BC Ferries has the largest fleet of vehicle ferry vessels in the world. There are 36 vessels, ranging from small 16-car ferries up to 470-car superferries. All of the vessels in use by BC Ferries are roll-on/roll-off car ferries. Most of the major vessels are based on similar designs, which are aggregated into classes of ferries:


title: BC Ferries

text: In 2019, BC started a $200 million program to acquire four hybrid/electric ferries (800 kWh each) to service three routes.


title: BC Ferries

text: On August 9, 1979, "Queen of Alberni" was transiting through Active Pass when it ran aground on Galiano Island, tipping fifteen degrees to starboard. Several large commercial vehicles on board the vessel at the time were damaged. No persons were injured, but a racehorse on board died. This accident suspended all C-class vessels from travelling on Route 1 or any of the Southern Gulf Islands routes.


title: BC Ferries

text: In June 1989, the vessel slammed into the loading dock at Departure Bay at about eight knots. Six people sustained slight injuries, including one who fell down a stairway. The ship received a scrape and some onboard vehicles were damaged.


title: BC Ferries

text: On March 12, 1992, at 8:08am (16:08 UTC), "Queen of Alberni" collided with the Japanese freighter "Shinwa Maru" southwest of Tsawwassen. The collision occurred in heavy fog, with both vessels suffering minor damage. Injuries included 2 serious and 25 minor injuries for the 260 people on the ferry, while none of the 11 people aboard the freighter received injuries.


title: BC Ferries

text: On August 25, 1966, the "Queen of Burnaby" broke her mooring at Departure Bay terminal while engines were being run in the early morning. The variable-pitch propellers were not left in the neutral position as was standard, and no crew was present on the bridge. The ferry was recovered after the anchor was dropped and the captain was shuttled to the vessel, and all sailing continued with no change of scheduling.


title: BC Ferries

text: On October 19, 1980, "Queen of Coquitlam" sustained $3 million of damage on tipping in the Burrard Shipyard floating drydock.


title: BC Ferries

text: On August 12, 1985, three occupants were killed when "Queen of Cowichan" ran over a pleasure boat near the Horseshoe Bay terminal. The BC Court of Appeal found the Cowichan two thirds at fault and ordered that $500,000 in damages be paid.


title: BC Ferries

text: On October 19, 2019, a crew member was significantly injured after being hit by the vessel's bow door which was having trouble opening at Horseshoe Bay terminal. The next round trip to Departure Bay and back was subsequently cancelled.


title: BC Ferries

text: On April 18, 2018, "Queen of Cumberland" crew members were injured during a safety drill at Swartz Bay ferry terminal. When a hoist cable parted on the ship's davit, a rescue boat holding two occupants fell about into the water. The boat was damaged and the individuals injured, one seriously.


title: BC Ferries

text: On September 20, 1978, "Queen of the Islands" rammed the Saltery Bay dock causing $495,000 worth of damage.


title: BC Ferries

text: On November 2, 2013, "Queen of Nanaimo" was pushed off course by severe weather as it was leaving the berth at Village Bay, Mayne Island. It damaged a private dock, and no one was injured. There was damage to the ship and all Tsawwassen–Gulf Islands sailings had to be cancelled while it was repaired.


title: BC Ferries

text: On October 20, 1971, "Queen of New Westminster" pulled out of its berth at the Departure Bay terminal while vehicle loading was in progress. A car and its two occupants fell into the water. Both of the vehicle's occupants were rescued.


title: BC Ferries

text: In a similar incident, on August 13, 1992, the "Queen of New Westminster" pulled out of its berth at the Departure Bay terminal while vehicle loading ramps were still lowered and resting on the ship. Three people were killed, including two children, one was seriously injured, and two others received minor injuries when a van containing 6 people fell from the upper deck onto the lower car deck and finally into the sea below. The van had been stopped and instructed to wait on the loading ramp by terminal crew members. The Transportation Safety Board of Canada determined that the accident was caused by the vessel not properly following departing procedures and secondarily due to poor communication between terminal and ship crew members.


title: BC Ferries

text: On December 17, 1974, the formerly named "Queen of Surrey" was withdrawn to repair damage from a fire in an electrical panel.


title: BC Ferries

text: On March 22, 2006, "Queen of the North" sank south of Prince Rupert, British Columbia, when it struck Gil Island at approximately 1:00 a.m. Two people from 100 Mile House went missing. BC Ferries CEO David Hahn said, "There is a real possibility that they went down with the ship." It is unlikely that it will be possible to salvage "Queen of the North".


title: BC Ferries

text: Officials have determined the cause of the accident was human error by three BC Ferries employees neglecting their navigational duties. Charges of criminal negligence causing death were considered, and a class action lawsuit for the passengers is proceeding while the Ferry and Marine Union seeks to reinstate the fired crew who failed to provide information to the $1 million TSB enquiry.


title: BC Ferries

text: On June 30, 2005, at about 10:10 a.m. (17:10 UTC), the vessel "Queen of Oak Bay", on the Nanaimo–Horseshoe Bay (Trans-Canada Highway) ferry route, lost power four minutes before it was to dock at the Horseshoe Bay terminal. The vessel became adrift, unable to change speed but able to steer with the rudders. The horn was blown steadily, and an announcement telling passengers to brace for impact was made minutes before the ship slowly ran into the nearby Sewell's Marina, where it destroyed or damaged 28 pleasure crafts and subsequently went aground a short distance from the shore. No casualties or injuries were reported.


title: BC Ferries

text: On July 1, 2005, BC Ferries issued a statement that Transport Canada, the Transportation Safety Board, and Lloyd's Register of Shipping were reviewing the control and mechanical systems on board to find a fault. An inspection revealed minimal damage to the ship, with only some minor damage to a metal fender, paint scrapes to the rudder, and some minor scrapes to one blade of a propeller.


title: BC Ferries

text: On July 7, BC Ferries concluded that a missing cotter pin was to blame. The pin normally retained a nut on a linkage between an engine speed governor and the fuel control for one of the engines. Without the pin, the nut fell off and the linkage separated, causing the engine, clutches, and propellers to increase in speed until overspeed safety devices activated and shut down the entire propulsion system. The faulty speed governor had been serviced 17 days before the incident during a $35-million upgrade, and the cotter pin had not been properly replaced at that time.


title: BC Ferries

text: "Queen of Oak Bay" was quickly repaired and tested at sea trials. She returned to regular service on July 8. A complete investigation report consisting of a 14-page Divisional Inquiry and a 28-page Engineering Incident Investigation was released in September 2006.


title: BC Ferries

text: The Transportation Safety Board's Marine Investigation Report, released on September 6, 2007, indicated that "inadequacies in BC Ferries' procedures on safety-critical maintenance tasks and on ship handling during berthing operations" were major contributing factors to the accident. It appears that insufficient oversight of work done by contractors also played a role in the accident.


title: BC Ferries

text: On August 25, 1982, the "MV Queen of Prince Rupert" departed from McLoughlin Bay (Bella Bella, Campbell Island) several hours behind schedule, headed for Ocean Falls. In an effort to make up for some of the lost time, the captain ordered for the ship to be taken through Gunboat Passage, a narrow and dangerous shortcut. Gunboat Passage would have allowed for the vessel to entirely skip having to go south all the way around Denny Island, before going north again, up to Ocean Falls. This shortcut allows for a ship to sail between Denny Island and Cunningham Island, cutting the sailing time to Ocean Falls approximately in half.


title: BC Ferries

text: When the "Queen of Prince Rupert" entered Gunboat Passage, several passengers aboard the ship went immediately to the Purser's Office to warn the crew that they were going the wrong way, down an unsafe passage. The Purser informed them that the captain knew what he was doing, and that everything was going as planned. Soon after, the ship ran aground in a particularly tight part of the channel. The captain quickly had the ship removed from the rock, then continued forward and ran aground again, on the same rock, further damaging the hull. This time, the ship would not budge, and the crew and passengers had to wait for 12 hours before being pulled away by a variety of tugboats, fishing boats, and a Coast Guard ship.


title: BC Ferries

text: The captain turned the "Queen of Prince Rupert" around and opted to sail around Denny Island that time.


title: BC Ferries

text: On the morning of February 6, 1992, "Queen of Saanich" and the passenger catamaran "Royal Vancouver" collided in heavy fog near the northern entrance of Active Pass. The bow doors of the Saanich were damaged. Aboard the "Royal Vancouver", 23 passengers and four crew sustained largely minor injuries. Although both vessels were operating their radar systems, the "Royal Vancouver" was found negligent in this regard.


title: BC Ferries

text: On May 12, 2003, the vessel was disabled as a result of an engine room fire. "Queen of Capilano" was dispatched and tethered to "Queen of Surrey" while tugboats were dispatched. The vessel was then towed back to shore. None of the 318 passengers were injured, but several crew members were treated for minor injuries. Some buckling of the main car deck resulted from the heat of the fire, but no vehicles were damaged in the incident.


title: BC Ferries

text: On March 26, 2019, the 7:30am sailing from Horseshoe Bay of the vessel had an incident while docking at Langdale at 8:10am. The ship collided with a terminal structure and damaged its leading end. The bow of the ferry subsequently became lodged on the structure, causing severe delays, with all following vehicle sailings that day cancelled until the late evening, when relief could be provided. Passenger service was offered by water taxi for walk-in passengers.


title: BC Ferries

text: On August 2, 1970, the Soviet freighter "Sergey Yesenin" collided with "Queen of Victoria" in Active Pass, slicing through the middle of the ferry, days after its return to service following stretching. Three people were killed, and damage was estimated at over $1 million (1970 dollars). The Soviet ship did not have permission to be in Active Pass, and as such, the Soviet government compensated BC Ferries.


title: BC Ferries

text: In 1972, while in Active Pass and within metres of the site of the 1970 collision, "Queen of Victoria" was disabled by a fire in the engine room.


title: BC Ferries

text: On January 23, 1966, "Langdale Queen" ran over a rowboat at Horseshoe Bay, on which both occupants survived.


title: BC Ferries

text: On November 7, 1995, "Mayne Queen" departed from Snug Cove and ran into a neighbouring marina, heavily damaging a floating dock in addition to 12 small pleasure boats, one of which sank. The crash was primarily attributed to human error and while transferring steering and power control from one control panel to the other located in the ship. The vessel's captain was also inexperienced with "Mayne Queen" and normally piloted other vessels. The captain then promptly left the scene of the accident after the incident without conducting a proper damage assessment.


title: BC Ferries

text: On August 12, 1996, "Mayne Queen" departed Swartz Bay terminal and ran aground off Piers Island after losing steering control. The grounding occurred while performing a regular weekly test of the batteries for the steering control system. A crew member overheard there was going to be a test, and in an attempt to be helpful, and without direction, cut all power from the vessel's steering batteries, as he had done at night when the ship was stored. However, he did not realize that the test in question only required the removal of a battery charger and that his assistance was neither requested nor required. No one was injured in the incident, and the vessel was assisted off the rocks at high tide, but it suffered extensive damage to its propulsion system, having two of the four steering and propulsion pods for the right-angle drives sheared off and one of the two remaining pods suffering propeller damage.


title: BC Ferries

text: On April 5, 1962, the formerly named "Chinook" ran aground on a submerged reef east of Snake Island in dense fog.


title: BC Ferries

text: On July 17, 1962, a time-bomb, comprising three sticks of dynamite, likely planted by the Freedomites, destroyed a locker on the "Chinook".


title: BC Ferries

text: On July 14, 1974, "Sechelt Queen" collided with a pleasure craft in Active Pass, causing some damage, but did not stop to render assistance.


title: BC Ferries

text: On July 27, 2005, a man travelling to Mayne Island missed his ferry, so he got on the Spirit of British Columbia and jumped off as the ferry was approaching Active Pass. The man refused rescue assistance from crew members, and was later banned from travelling with BC Ferries.


title: BC Ferries

text: On April 27, 2019, the "Spirit of British Columbia" was damaged while docking at Tsawwassen ferry terminal during heavy winds.


title: BC Ferries

text: On September 14, 2000, "Spirit of Vancouver Island" collided with the "Star Ruby" while attempting to overtake the vessel in a narrow channel. The collision occurred approximately from the Swartz Bay Terminal, from which the ferry had departed. "Spirit of Vancouver Island" struck "Star Ruby" on its port side, causing the pleasure craft to flip over and eventually right itself, though swamped and heavily damaged. According to the accident report, the pleasure craft ignored warning blasts from the approaching ferry and made a sharp turn towards the ferry just prior to impact. Two passengers aboard "Star Ruby" later died as a result of injuries sustained by the collision.


title: BC Ferries

text: On July 21, 2003, "Spirit of Vancouver Island" collided with the dock at Swartz Bay. Four passengers suffered minor injuries. The accident caused tens of thousands of dollars of damage to the dock and the ship.


title: BC Ferries

text: On October 9, 2009, a standby generator on "Spirit of Vancouver Island" caught fire on an early morning sailing out of Swartz Bay Terminal. No one was injured in the incident, but it caused major delays in the ferry system because of the already large volume of traffic for Thanksgiving weekend. Eight sailings were cancelled that day, and the ship remained out of service for the weekend.


title: BC Ferries

text: On August 31, 2018, two crew members were injured during an early morning safety drill at Swartz Bay ferry terminal when the ship's davit malfunctioned, causing a rescue boat to flip, dropping the two occupants into the water. The coxswain fell about , but the bowman held on while the boat continued to descend, reducing the fall to about .


title: BC Ferries

text: On April 18, 2020, at 4:26pm (16:26 UTC), the vessel, travelling at an approximate speed of 5.4 knots, struck the concrete abutment on the wall of berth 3 at Tsawwassen ferry terminal. Although damage was minor, the offloading of vehicles on the upper car deck and foot passengers was delayed until 6:02pm. Passengers were required to disembark from the main car deck instead of the overhead walkway. Offloading of vehicles on the main car deck began at 8:58pm.


title: BC Ferries

text: On May 5, 2011, "Coastal Celebration" damaged the dock at Swartz Bay after the vessel reversed into it for roughly . An investigation found that this was due to an error on the bridge. No one was hurt in the incident. However, damage to "Coastal Celebration" and the berth at Swartz Bay cost CAN$470,000.


title: BC Ferries

text: On November 4, 2015, while the ship was sailing from Tsawwassen to Swartz Bay, a man launched one of "Coastal Celebration"s 100-person life rafts and jumped overboard. The man then swam to Galiano Island while the ferry recovered the life raft and launched rescue craft to recover the man. The man was later arrested on the island.


title: BC Ferries

text: On December 17, 2018, the Coastal Celebration rescued a man from a sinking vessel near Moresby Passage in dark and stormy conditions. All remaining sailings from Tsawwassen to Swartz Bay were cancelled that night.


title: BC Ferries

text: On December 20, 2011, at 14:50 (21:50 UTC), "Coastal Inspiration" crashed into the Duke Point terminal, causing minor injuries to one passenger and crew member. The collision damaged the loading ramp, and foot passengers were held up for an hour before being unloaded; the vessel was rerouted to Departure Bay to unload its vehicle traffic. An electrical component failure in the propulsion control system was blamed for the crash. The ferry was taken out of service for repairs before resuming service on January 20, 2012. The damage caused the Duke Point terminal to be closed for five months, resulting in all services from Tsawwassen being rerouted into Departure Bay. The terminal reopened for service on May 1, 2012.


title: BC Ferries

text: On January 9, 2007, "Quinsam" was loading traffic from Nanaimo to Gabriola Island when it unexpectedly pulled out of its berth. A pickup truck on the boarding ramp plunged into the water below. Ferry workers were able to warn the truck's lone occupant, who was able to escape before the vehicle fell.


title: Pentium 4

text: Pentium 4 is a series of single-core CPUs for desktops, laptops and entry-level servers manufactured by Intel. The processors were shipped from November 20, 2000 until August 8, 2008. The production of Netburst processors was active from 2000 until May 21, 2010.


title: Pentium 4

text: All Pentium 4 CPUs are based on the NetBurst microarchitecture. The Pentium 4 "Willamette" (180 nm) introduced SSE2, while the "Prescott" (90 nm) introduced SSE3. Later versions introduced Hyper-Threading Technology (HTT).


title: Pentium 4

text: The first Pentium 4-branded processor to implement 64-bit was the "Prescott" (90 nm) (February 2004), but this feature was not enabled. Intel subsequently began selling 64-bit Pentium 4s using the ""E0" revision" of the Prescotts, being sold on the OEM market as the Pentium 4, model F. The E0 revision also adds eXecute Disable (XD) (Intel's name for the NX bit) to Intel 64. Intel's official launch of Intel 64 (under the name EM64T at that time) in mainstream desktop processors was the N0 stepping Prescott-2M.


title: Pentium 4

text: Intel also marketed a version of their low-end Celeron processors based on the NetBurst microarchitecture (often referred to as "Celeron 4"), and a high-end derivative, Xeon, intended for multi-socket servers and workstations. In 2005, the Pentium 4 was complemented by the dual-core-brands Pentium D and Pentium Extreme Edition.


title: Pentium 4

text: In benchmark evaluations, the advantages of the NetBurst microarchitecture were unclear. With carefully optimized application code, the first Pentium 4s outperformed Intel's fastest Pentium III (clocked at 1.13 GHz at the time), as expected. But in legacy applications with many branching or x87 floating-point instructions, the Pentium 4 would merely match or run slower than its predecessor. Its main downfall was a shared unidirectional bus. The NetBurst microarchitecture consumed more power and emitted more heat than any previous Intel or AMD microarchitectures.


title: Pentium 4

text: As a result, the Pentium 4's introduction was met with mixed reviews: Developers disliked the Pentium 4, as it posed a new set of code optimization rules. For example, in mathematical applications, AMD's lower-clocked Athlon (the fastest-clocked model was clocked at 1.2 GHz at the time) easily outperformed the Pentium 4, which would only catch up if software was re-compiled with SSE2 support. Tom Yager of "Infoworld" magazine called it "the fastest CPU - for programs that fit entirely in cache". Computer-savvy buyers avoided Pentium 4 PCs due to their price premium, questionable benefit, and initial restriction to Rambus' RDRAM. In terms of product marketing, the Pentium 4's singular emphasis on clock frequency (above all else) made it a marketer's dream. The result of this was that the NetBurst micro architecture was often referred to as a marchitecture by various computing websites and publications during the life of the Pentium 4. It was also called "NetBust," a term popular with reviewers who reflected negatively upon the processor's performance.


title: Pentium 4

text: The two classical metrics of CPU performance are IPC (instructions per cycle) and clock speed. While IPC is difficult to quantify due to dependence on the benchmark application's instruction mix, clock speed is a simple measurement yielding a single absolute number. Unsophisticated buyers would simply consider the processor with the highest clock speed to be the best product, and the Pentium 4 had the fastest clock speed. Because AMD's processors had slower clock speeds, it countered Intel's marketing advantage with the "megahertz myth" campaign. AMD product marketing used a "PR-rating" system, which assigned a merit value based on relative performance to a baseline machine.


title: Pentium 4

text: At the launch of the Pentium 4, Intel stated that NetBurst-based processors were expected to scale to 10 GHz after several fabrication process generations. However, the clock speed of processors using the NetBurst micro architecture reached a maximum of 3.8 GHz. Intel had not anticipated a rapid upward scaling of transistor power leakage that began to occur as the die reached the 90 nm lithography and smaller. This new power leakage phenomenon, along with the standard thermal output, created cooling and clock scaling problems as clock speeds increased. Reacting to these unexpected obstacles, Intel attempted several core redesigns ("Prescott" most notably) and explored new manufacturing technologies, such as using multiple cores, increasing FSB speeds, increasing the cache size, and using a longer instruction pipeline along with higher clock speeds.


title: Pentium 4

text: The code cache was replaced by a trace cache which contained decoded microoperations rather than instructions with advantage of eliminating instruction decoding bottleneck so that the design can use RISC technology. This came with a disadvantage of less compact cache taking up more chip space and consuming power.


title: Pentium 4

text: These solutions failed, and from 2003 to 2005, Intel shifted development away from NetBurst to focus on the cooler-running Pentium M microarchitecture. On January 5, 2006, Intel launched the Core processors, which put greater emphasis on energy efficiency and performance per clock cycle. The final NetBurst-derived products were released in 2007, with all subsequent product families switching exclusively to the Core microarchitecture.


title: Pentium 4

text: According to Bob Bentley, presenting on behalf of Intel at the 38th annual Design Automation Conference, "The microarchitecture of the Pentium 4 processor is significantly more complex than any previous IA-32 microprocessor, so the challenge of validating the logical correctness of the design in a timely fashion was indeed a daunting one." He hired a team of 60 recent graduates to help with testing and validation.


title: Pentium 4

text: Pentium 4 processors have an integrated heat spreader (IHS) that prevents the die from accidentally being damaged when mounting and unmounting cooling solutions. Prior to the IHS, a CPU shim was sometimes used by people worried about damaging the core. Overclockers sometimes removed the IHS from Socket 423 and Socket 478 chips to allow for more direct heat transfer. On Socket 478 Prescott processors and processors using the Socket LGA 775 (Socket T) interface, the IHS is directly soldered to the die or dies, making it difficult to remove.


title: Pentium 4

text: Willamette, the project codename for the first NetBurst microarchitecture implementation, experienced long delays in the completion of its design process. The project was started in 1998, when Intel saw the Pentium II as their permanent line. At that time, the Willamette core was expected to operate at frequencies up to about 1 GHz. However, the Pentium III was released while Willamette was still being finished. Due to the radical differences between the P6 and NetBurst microarchitectures, Intel could not market Willamette as a Pentium III, so it was marketed as the Pentium 4.


title: Pentium 4

text: On November 20, 2000, Intel released the Willamette-based Pentium 4 clocked at 1.4 and 1.5 GHz. Most industry experts regarded the initial release as a stopgap product, introduced before it was truly ready. According to these experts, the Pentium 4 was released because the competing Thunderbird-based AMD Athlon was outperforming the aging Pentium III, and further improvements to the Pentium III were not yet possible. This Pentium 4 was produced using a 180 nm process and initially used Socket 423 (also called socket W, for "Willamette"), with later revisions moving to Socket 478 (socket N, for "Northwood"). These variants were identified by the Intel product codes 80528 and 80531 respectively.


title: Pentium 4

text: On the test bench, the Willamette was somewhat disappointing to analysts in that not only was it unable to outperform the Athlon and the highest-clocked Pentium IIIs in all testing situations, but it was not superior to the budget segment's AMD Duron. Although introduced at prices of $644 (1.4 GHz) and $819 (1.5 GHz) for 1000 quantities to OEM PC manufacturers (prices for models for the consumer market varied by retailer), it sold at a modest but respectable rate, handicapped somewhat by the requirement for relatively fast yet expensive Rambus Dynamic RAM (RDRAM). The Pentium III remained Intel's top selling processor line, with the Athlon also selling slightly better than the Pentium 4. While Intel bundled two RDRAM modules with each boxed Pentium 4, it did not facilitate Pentium 4 sales and was not considered a true solution by many.


title: Pentium 4

text: In January 2001, a still slower 1.3 GHz model was added to the range, but over the next twelve months, Intel gradually started reducing AMD's leadership in performance. In April 2001 a 1.7 GHz Pentium 4 was launched, the first model to provide performance clearly superior to the old Pentium III. July saw 1.6 and 1.8 GHz models and in August 2001, Intel released 1.9 and 2 GHz Pentium 4s. In the same month, they released the 845 chipset that supported much cheaper PC133 SDRAM instead of RDRAM. The fact that SDRAM was so much cheaper caused the Pentium 4's sales to grow considerably. The new chipset allowed the Pentium 4 to quickly replace the Pentium III, becoming the top-selling mainstream processor on the market.


title: Pentium 4

text: The Willamette code name is derived from the Willamette Valley region of Oregon, where a large number of Intel's manufacturing facilities are located.


title: Pentium 4

text: In January 2002, Intel released Pentium 4s with a new core code named "Northwood" at speeds of 1.6 GHz, 1.8 GHz, 2 GHz and 2.2 GHz. "Northwood" (product code 80532) combined an increase in the L2 cache size from 256 KB to 512 KB (increasing the transistor count from 42 million to 55 million) with a transition to a new 130 nm fabrication process. Making the processor out of smaller transistors means that it can run at higher clock speeds and produce less heat. In the same month boards utilizing the 845 chipset were released with enabled support for DDR SDRAM which provided double the bandwidth of PC133 SDRAM, and alleviated the associated high costs of using Rambus RDRAM for maximal performance with Pentium 4.


title: Pentium 4

text: A 2.4 GHz Pentium 4 was released on April 2, 2002, and the bus speed increased from 400 MT/s to 533 MT/s (133 MHz physical clock) for the 2.26 GHz, 2.4 GHz, and 2.53 GHz models in May, 2.66 GHz and 2.8 GHz models in August, and 3.06 GHz model in November. With Northwood, the Pentium 4 came of age. The battle for performance leadership remained competitive (as AMD introduced faster versions of the Athlon XP) but most observers agreed that the fastest-clocked Northwood-based Pentium 4 was usually ahead of its rival. This was particularly so in mid-2002, when AMD's changeover to its 130 nm production process did not help the initial "Thoroughbred A" revision Athlon XP CPUs to clock high enough to overcome the advantages of Northwood in the 2.4 to 2.8 GHz range.


title: Pentium 4

text: The 3.06 GHz Pentium 4 enabled Hyper-Threading Technology that was first supported in Foster-based Xeons. This began the convention of virtual processors (or virtual cores) under x86 by enabling multiple threads to be run at the same time on the same physical processor. By shuffling two (ideally differing) program instructions to simultaneously execute through a single physical processor core, the goal is to best utilize processor resources that would have otherwise been unused from the traditional approach of having these single instructions wait for each other to execute singularly through the core. This initial 3.06 GHz 533FSB Pentium 4 Hyper-Threading enabled processor was known as Pentium 4 HT and was introduced to mass market by Gateway in November 2002.