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−0 (number)
Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are identical. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the ''sign and magnitude'' and ''ones' complement'' signed number representations for integers, and in most floating-point number representations. The number 0 is usually encoded as +0, but can be represented by either +0 or −0. The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Real arithmetic with signed zeros can be considered a variant of the extended real number line such that 1/−0 = −∞ and 1/+0 = +∞; division is only undefi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero
0 (zero) is a number representing an empty quantity. In place-value notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ... such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by Multiplication, multiplying digits to the left of 0 by the radix, usually by 10. As a number, 0 fulfills a central role in mathematics as the additive identity of the integers, real numbers, and other algebraic structures. Common names for the number 0 in English are ''zero'', ''nought'', ''naught'' (), ''nil''. In contexts where at least one adjacent digit distinguishes it from the O, letter O, the number is sometimes pronounced as ''oh'' or ''o'' (). Informal or slang terms for 0 include ''zilch'' and ''zip''. Historically, ''ought'', ''aught'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Kahan
William "Velvel" Morton Kahan (born June 5, 1933) is a Canadian mathematician and computer scientist, who received the Turing Award in 1989 for "''his fundamental contributions to numerical analysis''", was named an ACM Fellow in 1994, and inducted into the National Academy of Engineering in 2005. Biography Born to a Canadian Jewish family, he attended the University of Toronto, where he received his bachelor's degree in 1954, his master's degree in 1956, and his Ph.D. in 1958, all in the field of mathematics. Kahan is now emeritus professor of mathematics and of electrical engineering and computer sciences (EECS) at the University of California, Berkeley. Kahan was the primary architect behind the IEEE 754-1985 standard for floating-point computation (and its radix-independent follow-on, IEEE 854). He has been called "The Father of Floating Point", since he was instrumental in creating the original IEEE 754 specification. Kahan continued his contributions to the IEEE 754 revisio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Punning
In computer science, a type punning is any programming technique that subverts or circumvents the type system of a programming language in order to achieve an effect that would be difficult or impossible to achieve within the bounds of the formal language. In C and C++, constructs such as pointer type conversion and union — C++ adds reference type conversion and reinterpret_cast to this list — are provided in order to permit many kinds of type punning, although some kinds are not actually supported by the standard language. In the Pascal programming language, the use of records with variants may be used to treat a particular data type in more than one manner, or in a manner not normally permitted. Sockets example One classic example of type punning is found in the Berkeley sockets interface. The function to bind an opened but uninitialized socket to an IP address is declared as follows: int bind(int sockfd, struct sockaddr *my_addr, socklen_t addrlen); The bind funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java Programming Language
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers ''write once, run anywhere'' ( WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax of Java is similar to C and C++, but has fewer low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as reflection and runtime code modification) that are typically not available in traditional compiled languages. , Java was one of the most popular programming languages in use according to GitHub, particularly for client–server web applications, with a reported 9 million developers. Java was originally developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exception Handling
In computing and computer programming, exception handling is the process of responding to the occurrence of ''exceptions'' – anomalous or exceptional conditions requiring special processing – during the execution of a program. In general, an exception breaks the normal flow of execution and executes a pre-registered ''exception handler''; the details of how this is done depend on whether it is a hardware or software exception and how the software exception is implemented. Exception handling, if provided, is facilitated by specialized programming language constructs, hardware mechanisms like interrupts, or operating system (OS) inter-process communication (IPC) facilities like signals. Some exceptions, especially hardware ones, may be handled so gracefully that execution can resume where it was interrupted. Definition The definition of an exception is based on the observation that each procedure has a precondition, a set of circumstances for which it will terminate "normal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indeterminate Form
In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. More specifically, an indeterminate form is a mathematical expression involving at most two of 0~, 1 or \infty, obtained by applying the algebraic limit theorem in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being sought. A limit confirmed to be infinity is not indeterminate since it has been determined to have a specific value (infinity). The term was originally introduced by Cauchy's student Moigno in the middle of the 19th century. There are seven indeterminate forms which are typically cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Underflow
The term arithmetic underflow (also floating point underflow, or just underflow) is a condition in a computer program where the result of a calculation is a number of more precise absolute value than the computer can actually represent in memory on its central processing unit (CPU). Arithmetic underflow can occur when the true result of a floating point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating point number in the target datatype. Underflow can in part be regarded as negative overflow of the exponent of the floating point value. For example, if the exponent part can represent values from −128 to 127, then a result with a value less than −128 may cause underflow. Storing values that are too low in an integer variable (e.g., attempting to store −1 in an unsigned integer) is properly referred to as integer , or more broadly, ''integer wraparound''. The term ''underflow'' normally refers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significand
The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. Depending on the interpretation of the exponent, the significand may represent an integer or a fraction. Example The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10−2 power term, also called characteristics, where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic: : 123.45 = 12345 × 10−2. The same value can also be represented in normalized form with 1.2345 as the fractional coefficient, and +2 as the exponent (and 10 as the base): : 123.45 = 1.2345 × 10+2. Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form. For base 2, this 1.xxxx form is also called a normalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 754 Single Negative Zero
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operations center in Piscataway, New Jersey. The mission of the IEEE is ''advancing technology for the benefit of humanity''. The IEEE was formed from the amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers in 1963. Due to its expansion of scope into so many related fields, it is simply referred to by the letters I-E-E-E (pronounced I-triple-E), except on legal business documents. , it is the world's largest association of technical professionals with more than 423,000 members in over 160 countries around the world. Its objectives are the educational and technical advancement of electrical and electronic engineering, telecommunications, computer engineering and similar disciplines. History Origins ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signed Magnitude
In computing, signed number representations are required to encode negative numbers in binary number systems. In mathematics, negative numbers in any base are represented by prefixing them with a minus sign ("−"). However, in RAM or CPU registers, numbers are represented only as sequences of bits, without extra symbols. The four best-known methods of extending the binary numeral system to represent signed numbers are: sign–magnitude, ones' complement, two's complement, and offset binary. Some of the alternative methods use implicit instead of explicit signs, such as negative binary, using the base −2. Corresponding methods can be devised for other bases, whether positive, negative, fractional, or other elaborations on such themes. There is no definitive criterion by which any of the representations is universally superior. For integers, the representation used in most current computing devices is two's complement, although the Unisys ClearPath Dorado series mainframes u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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