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Integer Square Root
In number theory, the integer square root (isqrt) of a non-negative integer is the non-negative integer which is the greatest integer less than or equal to the square root of , \operatorname(n) = \lfloor \sqrt n \rfloor. For example, \operatorname(27) = \lfloor \sqrt \rfloor = \lfloor 5.19615242270663 ... \rfloor = 5. Introductory remark Let y and k be non-negative integers. Algorithms that compute (the decimal representation of) \sqrt y run forever on each input y which is not a perfect square. The square roots of the perfect squares (e.g., 0, 1, 4, 9, 16) are integers. In all other cases, the square roots of positive integers are irrational numbers. Algorithms that compute \lfloor \sqrt y \rfloor do not run forever. They are nevertheless capable of computing \sqrt y up to any desired accuracy k. Choose any k and compute \lfloor \sqrt \rfloor. For example (setting y = 2): \begin & k = 0: \lfloor \sqrt \rfloor = \lfloor \sqrt \rfloor = 1 \\ & k = 1: \lfloor \sqrt \rfloo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Euclidean Division
In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder exist and are unique, under some conditions. Because of this uniqueness, ''Euclidean division'' is often considered without referring to any method of computation, and without explicitly computing the quotient and the remainder. The methods of computation are called integer division algorithms, the best known of which being long division. Euclidean division, and algorithms to compute it, are fundamental for many questions concerning integers, such as the Euclidean algorithm for finding the greatest common divisor of two integers, and modular arithmetic, for which only remainders are considered. The operation consisting of computing only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Arbitrary-precision Arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are potentially limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision. Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required. It should ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Access Modifiers
Access modifiers (or access specifiers) are keywords in object-oriented languages that set the accessibility of classes, methods, and other members. Access modifiers are a specific part of programming language syntax used to facilitate the encapsulation of components. In C++, there are only three access modifiers. C# extends the number of them to six, while Java has four access modifiers, but three keywords for this purpose. In Java, having no keyword before defaults to the package-private modifier. When the class is declared as public, it is accessible to other classes defined in the same package as well as those defined in other packages. This is the most commonly used specifier for classes. However, a class itself cannot be declared as private. If no access specifier is stated, the default access restrictions will be applied. The class will be accessible to other classes in the same package but will be inaccessible to classes outside the package. When we say that a clas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Find First Set
In computer software and hardware, find first set (ffs) or find first one is a bit operation that, given an unsigned Word (computer architecture), machine word, designates the index or position of the least significant bit set to one in the word counting from the least significant bit position. A nearly equivalent operation is count trailing zeros (ctz) or number of trailing zeros (ntz), which counts the number of zero bits following the least significant one bit. The complementary operation that finds the index or position of the most significant set bit is log base 2, so called because it computes the binary logarithm . This is #Properties and relations, closely related to count leading zeros (clz) or number of leading zeros (nlz), which counts the number of zero bits preceding the most significant one bit. There are two common variants of find first set, the POSIX definition which starts indexing of bits at 1, herein labelled ffs, and the variant which starts indexing of bits at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Recursion (computer Science)
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursion, recursive problems by using function (computer science), functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. Most computer programming languages support recursion by allowing a function to call itself from within its own code. Some functional programming languages (for instance, Clojure) do not define any looping constructs but rely solely on recursion to repeatedly call code. It is proved in computability theory that these recursive-only languages are Turing complete; this means that they are as powerful (they can be used to solve the same problems) as imperative languages based on control structures such as and . Repeatedly calling a function from within itse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Power Of Two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number 2, two as the Base (exponentiation), base and integer as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^n(1). In the Hardy hierarchy, is exactly equal to H_(1). Powers of two with Sign (mathematics)#Terminology for signs, non-negative exponents are integers: , , and is two multiplication, multiplied by itself times. The first ten powers of 2 for non-negative values of are: :1, 2, 4, 8, 16 (number), 16, 32 (number), 32, 64 (number), 64, 128 (number), 128, 256 (number), 256, 512 (number), 512, ... By comparison, powers of two with negative exponents are fractions: for positive integer , is one half multiplied by itself times. Thus the first few negative powers of 2 are , , , , etc. Sometimes these are called ''inverse powers of two'' because each is the multiplicative inverse of a positive power of two. Base of the binary numeral sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
C++20
C20 or C-20 may refer to: Science and technology * Carbon-20 (C-20 or 20C), an isotope of carbon * C20, the smallest possible fullerene (a carbon molecule) * C20 (engineering), a mix of concrete that has a compressive strength of 20 newtons per square millimeter * Malignant neoplasm of rectum, a type of colorectal cancer (ICD-10 code: C20) * Caldwell 20 or North America Nebula, an emission nebula in the constellation Cygnus * IEC 60320 C20, a polarised, three pole socket electrical connector * C20 (Capacity, 20 hours), C100 (100 hours), battery capacity Transportation and military * Colt Canada C20 DMR, a Canadian designated marksman rifle * , a 1910 British C-class submarine * Sauber C20, a 2001 racing car * SL C20, a type of rolling stock used in the Stockholm metro * , a cruiser of the Royal Navy * C-20, the proposed in-service designation of the Fokker F-32 * C-20A/B/C/D/E, variants of the Gulfstream III * C-20F/G/H/J, variants of the Gulfstream IV * C20 is a version of the Alli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bit-length
Bit length or bit width is the number of binary digits, called bits, necessary to represent an unsigned integer as a binary number. Formally, the bit length of a natural number n \geq 0 is :\ell(n) = \lceil \log_2(n+1) \rceil where \log_2 is the binary logarithm and \lceil \cdot \rceil is the ceiling function. At their most fundamental level, digital computers and telecommunications devices (as opposed to analog devices) process data that is encoded in binary format. The binary format expresses data as an arbitrary length series of values with one of two choices: Yes/No, 1/0, True/False, etc., all of which can be expressed electronically as On/Off. For information technology applications, the amount of information being processed is an important design consideration. The term bit length is technical shorthand for this measure. For example, computer processors are often designed to process data grouped into words of a given length of bits (8 bit, 16 bit, 32 bit, 64 bit, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
