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Subnormal Number
In computer science, subnormal numbers are the subset of denormalized numbers (sometimes called denormals) that fill the underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than the smallest normal number is ''subnormal''. :: ''Usage note: in some older documents (especially standards documents such as the initial releases of IEEE 754 and the C language), "denormal" is used to refer exclusively to subnormal numbers. This usage persists in various standards documents, especially when discussing hardware that is incapable of representing any other denormalized numbers, but the discussion here uses the term subnormal in line with the 2008 revision of IEEE 754.'' In a normal floating-point value, there are no leading zeros in the significand ( mantissa); rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as ). Conversely, a denormalized floating point value has a significand w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten ( decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Division By Zero
In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as \tfrac, where is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number that, when multiplied by , gives (assuming a \neq 0); thus, division by zero is undefined. Since any number multiplied by zero is zero, the expression \tfrac is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to \tfrac is contained in Anglo-Irish philosopher George Berkeley's criticism of infinitesimal calculus in 1734 in '' The Analyst'' ("ghosts of departed quantities"). There are mathematical structures in which \tfrac is defined for some such as in the Riemann sphere (a model of the extended complex plane) and the Projectively extended real line; however, such structures do not satisfy e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Logarithmic Number System
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing. Overview In an LNS, a number, X, is represented by the logarithm, x, of its absolute value as follows: :X\rightarrow\, where s is a bit denoting the sign of X (s=0 if X>0 and s=1 if X A VHDL library for LNS hardware generation Computer arithmetic Digital signal processing [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Application Binary Interface
In computer software, an application binary interface (ABI) is an interface between two binary program modules. Often, one of these modules is a library or operating system facility, and the other is a program that is being run by a user. An ''ABI'' defines how data structures or computational routines are accessed in machine code, which is a low-level, hardware-dependent format. In contrast, an ''API'' defines this access in source code, which is a relatively high-level, hardware-independent, often human-readable format. A common aspect of an ABI is the calling convention, which determines how data is provided as input to, or read as output from, computational routines. Examples of this are the x86 calling conventions. Adhering to an ABI (which may or may not be officially standardized) is usually the job of a compiler, operating system, or library author. However, an application programmer may have to deal with an ABI directly when writing a program in a mix of programm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Mac OS X
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and laptop computers it is the second most widely used desktop OS, after Microsoft Windows and ahead of ChromeOS. macOS succeeded the classic Mac OS, a Mac operating system with nine releases from 1984 to 1999. During this time, Apple cofounder Steve Jobs had left Apple and started another company, NeXT, developing the NeXTSTEP platform that would later be acquired by Apple to form the basis of macOS. The first desktop version, Mac OS X 10.0, was released in March 2001, with its first update, 10.1, arriving later that year. All releases from Mac OS X 10.5 Leopard and after are UNIX 03 certified, with an exception for OS X 10.7 Lion. Apple's other operating systems (iOS, iPadOS, watchOS, tvOS, audioOS) are derivatives of macOS. A prominent pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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GNU Compiler Collection
The GNU Compiler Collection (GCC) is an optimizing compiler produced by the GNU Project supporting various programming languages, hardware architectures and operating systems. The Free Software Foundation (FSF) distributes GCC as free software under the GNU General Public License (GNU GPL). GCC is a key component of the GNU toolchain and the standard compiler for most projects related to GNU and the Linux kernel. With roughly 15 million lines of code in 2019, GCC is one of the biggest free programs in existence. It has played an important role in the growth of free software, as both a tool and an example. When it was first released in 1987 by Richard Stallman, GCC 1.0 was named the GNU C Compiler since it only handled the C programming language. It was extended to compile C++ in December of that year. Front ends were later developed for Objective-C, Objective-C++, Fortran, Ada, D and Go, among others. The OpenMP and OpenACC specifications are also supported in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Clang
Clang is a compiler front end for the C, C++, Objective-C, and Objective-C++ programming languages, as well as the OpenMP, OpenCL, RenderScript, CUDA, and HIP frameworks. It acts as a drop-in replacement for the GNU Compiler Collection (GCC), supporting most of its compilation flags and unofficial language extensions. It includes a static analyzer, and several code analysis tools. Clang operates in tandem with the LLVM compiler back end and has been a subproject of LLVM 2.6 and later. As with LLVM, it is free and open-source software under the Apache License 2.0 software license. Its contributors include Apple, Microsoft, Google, ARM, Sony, Intel, and AMD. Clang 14, the latest major version of Clang as of March 2022, has full support for all published C++ standards up to C++17, implements most features of C++20, and has initial support for the upcoming C++23 standard. Since v6.0.0, Clang compiles C++ using the GNU++14 dialect by default, which includes fea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Streaming SIMD Extensions
In computing, Streaming SIMD Extensions (SSE) is a single instruction, multiple data (SIMD) instruction set extension to the x86 architecture, designed by Intel and introduced in 1999 in their Pentium III series of Central processing units (CPUs) shortly after the appearance of Advanced Micro Devices (AMD's) 3DNow!. SSE contains 70 new instructions (65 unique mnemonics using 70 encodings), most of which work on single precision floating-point data. SIMD instructions can greatly increase performance when exactly the same operations are to be performed on multiple data objects. Typical applications are digital signal processing and graphics processing. Intel's first IA-32 SIMD effort was the MMX instruction set. MMX had two main problems: it re-used existing x87 floating-point registers making the CPUs unable to work on both floating-point and SIMD data at the same time, and it only worked on integers. SSE floating-point instructions operate on a new independent register set, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 series of instruction sets, the instruction sets found in most personal computers (PCs). Delaware General Corporation Law, Incorporated in Delaware, Intel ranked No. 45 in the 2020 Fortune 500, ''Fortune'' 500 list of the largest United States corporations by total revenue for nearly a decade, from 2007 to 2016 fiscal years. Intel supplies microprocessors for List of computer system manufacturers, computer system manufacturers such as Acer Inc., Acer, Lenovo, HP Inc., HP, and Dell Technologies, Dell. Intel also manufactures motherboard chipsets, network interface controllers and integrated circuits, flash memory, Graphics processing unit, graphics chips, Embedded system, embedded processors and other devices related to com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Streaming SIMD Extensions
In computing, Streaming SIMD Extensions (SSE) is a single instruction, multiple data (SIMD) instruction set extension to the x86 architecture, designed by Intel and introduced in 1999 in their Pentium III series of Central processing units (CPUs) shortly after the appearance of Advanced Micro Devices (AMD's) 3DNow!. SSE contains 70 new instructions (65 unique mnemonics using 70 encodings), most of which work on single precision floating-point data. SIMD instructions can greatly increase performance when exactly the same operations are to be performed on multiple data objects. Typical applications are digital signal processing and graphics processing. Intel's first IA-32 SIMD effort was the MMX instruction set. MMX had two main problems: it re-used existing x87 floating-point registers making the CPUs unable to work on both floating-point and SIMD data at the same time, and it only worked on integers. SSE floating-point instructions operate on a new independent register set, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |