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Unit In The Last Place
In computer science and numerical analysis, unit in the last place or unit of least precision (ulp) is the spacing between two consecutive floating-point numbers, i.e., the value the least significant digit (rightmost digit) represents if it is 1. It is used as a measure of accuracy in numeric calculations. Definition One definition is: In radix b with precision p, if b^e \le , x, x. Otherwise, \operatorname (x + 1) = x or \operatorname (x + 1) = x + \operatorname(x), depending on the value of the least significant digit and the exponent of x. This is demonstrated in the following Haskell code typed at an interactive prompt: > until (\x -> x x+1) (+1) 0 :: Float 1.6777216e7 > it-1 1.6777215e7 > it+1 1.6777216e7 Here we start with 0 in single precision and repeatedly add 1 until the operation does not change the value. Since the significand for a single-precision number contains 24 bits, the first integer that is not exactly representable is 224+1, and this value rounds to 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haskell (programming Language)
Haskell () is a general-purpose, statically-typed, purely functional programming language with type inference and lazy evaluation. Designed for teaching, research and industrial applications, Haskell has pioneered a number of programming language features such as type classes, which enable type-safe operator overloading, and monadic IO. Haskell's main implementation is the Glasgow Haskell Compiler (GHC). It is named after logician Haskell Curry. Haskell's semantics are historically based on those of the Miranda programming language, which served to focus the efforts of the initial Haskell working group. The last formal specification of the language was made in July 2010, while the development of GHC continues to expand Haskell via language extensions. Haskell is used in academia and industry. , Haskell was the 28th most popular programming language by Google searches for tutorials, and made up less than 1% of active users on the GitHub source code repository. History ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Epsilon
Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point arithmetic. This value characterizes computer arithmetic in the field of numerical analysis, and by extension in the subject of computational science. The quantity is also called macheps and it has the symbols Greek epsilon \varepsilon. There are two prevailing definitions. In numerical analysis, machine epsilon is dependent on the type of rounding used and is also called unit roundoff, which has the symbol bold Roman u. However, by a less formal, but more widely-used definition, machine epsilon is independent of rounding method and may be equivalent to u or 2u. Values for standard hardware arithmetics The following table lists machine epsilon values for standard floating-point formats. Each format uses round-to-nearest. Formal definition ''Rounding'' is a procedure for choosing the representation of a real number in a floating point number system. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Significant Bit
In computing, bit numbering is the convention used to identify the bit positions in a binary number. Bit significance and indexing In computing, the least significant bit (LSB) is the bit position in a binary integer representing the binary 1s place of the integer. Similarly, the most significant bit (MSB) represents the highest-order place of the binary integer. The LSB is sometimes referred to as the ''low-order bit'' or ''right-most bit'', due to the convention in positional notation of writing less significant digits further to the right. The MSB is similarly referred to as the ''high-order bit'' or ''left-most bit''. In both cases, the LSB and MSB correlate directly to the least significant digit and most significant digit of a decimal integer. Bit indexing correlates to the positional notation of the value in base 2. For this reason, bit index is not affected by how the value is stored on the device, such as the value's byte order. Rather, it is a property of the numeri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO/IEC 10967
ISO/IEC 10967, Language independent arithmetic (LIA), is a series of standards on computer arithmetic. It is compatible with ISO/IEC/IEEE 60559:2011, more known as IEEE 754-2008, and much of the specifications are for IEEE 754 special values (though such values are not required by LIA itself, unless the parameter ''iec559'' is true). It was developed by the working group ISO/IEC JTC1/SC22/WG11, which was disbanded in 2011. LIA consists of three parts: * Part 1: ''Integer and floating point arithmetic'', second edition published 2012. * Part 2: ''Elementary numerical functions'', first edition published 2001. * Part 3: ''Complex integer and floating point arithmetic and complex elementary numerical functions'', first edition published 2006. Parts Part 1 Part 1 deals with the basic integer and floating point datatypes (for multiple radices, including 2 and 10), but unlike IEEE 754-2008 not the representation of the values. Part 1 also deals with basic arithmetic, including compari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swift (programming Language)
Swift is a general-purpose, multi-paradigm, compiled programming language developed by Apple Inc. and the open-source community. First released in 2014, Swift was developed as a replacement for Apple's earlier programming language Objective-C, as Objective-C had been largely unchanged since the early 1980s and lacked modern language features. Swift works with Apple's Cocoa and Cocoa Touch frameworks, and a key aspect of Swift's design was the ability to interoperate with the huge body of existing Objective-C code developed for Apple products over the previous decades. It was built with the open source LLVM compiler framework and has been included in Xcode since version 6, released in 2014. On Apple platforms, it uses the Objective-C runtime library, which allows C, Objective-C, C++ and Swift code to run within one program. Apple intended Swift to support many core concepts associated with Objective-C, notably dynamic dispatch, widespread late binding, extensible programming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (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 b ... [...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] |
Boost C++ Libraries
Boost is a set of libraries for the C++ programming language that provides support for tasks and structures such as linear algebra, pseudorandom number generation, multithreading, image processing, regular expressions, and unit testing. It contains 164 individual libraries (as of version 1.76). All of the Boost libraries are licensed under the Boost Software License, designed to allow Boost to be used with both free and proprietary software projects. Many of Boost's founders are on the C++ standards committee, and several Boost libraries have been accepted for incorporation into the C++ Technical Report 1, the C++11 standard (e.g. smart pointers, thread, regex, random, ratio, tuple) and the C++17 standard (e.g. filesystem, any, optional, variant, string_view). The Boost community emerged around 1998, when the first version of the standard was released. It has grown continuously since then and now plays a big role in the standardization of C++. Even though there is no formal re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double-precision
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. Floating point is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754-2008 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 ''single precision'' and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language and first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000 and introduced new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 3.0, released in 2008, was a major revision that is not completely backward-compatible with earlier versions. Python 2 was discontinued with version 2.7.18 in 2020. Python consistently ranks as ... [...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] |
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