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Subnormal Number
In computer science, subnormal numbers are the subset of denormalized numbers (sometimes called denormals) that fill the arithmetic underflow, underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than the smallest positive normal number (computing), normal number is ''subnormal'', while ''denormal'' can also refer to numbers outside that range. Terminology In some older documents (especially standards documents such as the initial releases of IEEE 754-1985, IEEE 754 and ISO_9899, 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 754-2008, IEEE 754. In casual discussions the terms ''subnormal'' and ''denormal'' are often used interchangeably, in part because there ar ...
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Asymptotic
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates Limit of a function#Limits at infinity, tends to infinity. In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity. The word asymptote is derived from the Greek language, Greek ἀσύμπτωτος (''asumptōtos'') which means "not falling together", from ἀ Privative alpha, priv. + σύν "together" + πτωτ-ός "fallen". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve. There are three kinds of asymptotes: ''horizontal'', ''vertical'' and ''oblique''. For curves given by the graph of a function, graph of a function (mathematics), function , horizontal asymptotes are horizontal lines tha ...
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Application Binary Interface
An application binary interface (ABI) is an interface exposed by software that is defined for in-process machine code access. Often, the exposing software is a library, and the consumer is a program. An ABI is at a relatively low-level of abstraction. Interface compatibility depends on the target hardware and the software build toolchain. In contrast, an application programming interface (API) defines access in source code which is a relatively high-level, hardware-independent, and human-readable format. An API defines interface at the source code level, before compilation, whereas an ABI defines an interface to compiled code. API compatibility is generally the concern for system design and of the toolchain. However, a programmer may have to deal with an ABI directly when writing a program in a multiple languages or compilers. A complete ABI enables a program that supports an ABI to run without modification on multiple operating systems that provide the ABI. The targe ...
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Mac OS X
macOS, previously OS X and originally Mac OS X, is a Unix, Unix-based operating system developed and marketed by Apple Inc., Apple since 2001. It is the current operating system for Apple's Mac (computer), Mac computers. Within the market of Desktop computer, desktop and laptop computers, it is the Usage share of operating systems#Desktop and laptop computers, second most widely used desktop OS, after Microsoft Windows and ahead of all Linux distributions, including ChromeOS and SteamOS. , the most recent release of macOS is MacOS Sequoia, macOS 15 Sequoia, the 21st major version of macOS. Mac OS X succeeded classic Mac OS, the primary Mac operating systems, Macintosh operating system from 1984 to 2001. Its underlying architecture came from NeXT's NeXTSTEP, as a result of NeXT#1997–2006: Acquisition by Apple, Apple's acquisition of NeXT, which also brought Steve Jobs back to Apple. The first desktop version, Mac OS X 10.0, was released on March 24, 2001. Mac ...
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GNU Compiler Collection
The GNU Compiler Collection (GCC) is a collection of compilers from the GNU Project that support various programming languages, Computer architecture, 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 which is used for most projects related to GNU and the Linux kernel. With roughly 15 million lines of code in 2019, GCC is one of the largest 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), C programming language. It was extended to compile C++ in December of that year. Compiler#Front end, Front ends were later developed for Objective-C, Objective-C++, Fortran, Ada (programming language), Ada, Go (programming la ...
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Clang
Clang () is a compiler front end for the programming languages C, C++, Objective-C, Objective-C++, and the software frameworks OpenMP, OpenCL, RenderScript, CUDA, SYCL, and HIP. It acts as a drop-in replacement for the GNU Compiler Collection (GCC), supporting most of its compiling 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 2.0 software license. Its contributors include Apple, Microsoft, Google, ARM, Sony, Intel, and AMD. Clang 17, the latest major version of Clang as of October 2023, has full support for all published C++ standards up to C++17, implements most features of C++20, and has initial support for the C++23 standard. Since v16.0.0, Clang compiles C++ using the GNU++17 dialect by default, which includes features fro ...
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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 its 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 s ...
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Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California, and Delaware General Corporation Law, incorporated in Delaware. Intel designs, manufactures, and sells computer components such as central processing units (CPUs) and related products for business and consumer markets. It is one of the world's List of largest semiconductor chip manufacturers, largest semiconductor chip manufacturers by revenue, and ranked in the Fortune 500, ''Fortune'' 500 list of the List of largest companies in the United States by revenue, largest United States corporations by revenue for nearly a decade, from 2007 to 2016 Fiscal year, fiscal years, until it was removed from the ranking in 2018. In 2020, it was reinstated and ranked 45th, being the List of Fortune 500 computer software and information companies, 7th-largest technology company in the ranking. It was one of the first companies listed on Nasdaq. Intel supplies List of I ...
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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 its 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 s ...
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Timing Attack
In cryptography, a timing attack is a side-channel attack in which the attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms. Every logical operation in a computer takes time to execute, and the time can differ based on the input; with precise measurements of the time for each operation, an attacker can work backwards to the input. Finding secrets through timing information may be significantly easier than using cryptanalysis of known plaintext, ciphertext pairs. Sometimes timing information is combined with cryptanalysis to increase the rate of information leakage. Information can leak from a system through measurement of the time it takes to respond to certain queries. How much this information can help an attacker depends on many variables: cryptographic system design, the CPU running the system, the algorithms used, assorted implementation details, timing attack countermeasures, the accuracy of the timing measurements, e ...
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Instruction (computer Science)
In computer science, an instruction set architecture (ISA) is an abstract model that generally defines how software controls the CPU in a computer or a family of computers. A device or program that executes instructions described by that ISA, such as a central processing unit (CPU), is called an ''implementation'' of that ISA. In general, an ISA defines the supported Machine code, instructions, data types, Register (computer), registers, the hardware support for managing Computer memory, main memory, fundamental features (such as the memory consistency, addressing modes, virtual memory), and the input/output model of implementations of the ISA. An ISA specifies the behavior of machine code running on implementations of that ISA in a fashion that does not depend on the characteristics of that implementation, providing binary compatibility between implementations. This enables multiple implementations of an ISA that differ in characteristics such as Computer performance, performa ...
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Floating-point Unit
A floating-point unit (FPU), numeric processing unit (NPU), colloquially math coprocessor, is a part of a computer system specially designed to carry out operations on floating-point numbers. Typical operations are addition, subtraction, multiplication, division, and square root. Modern designs generally include a fused multiply-add instruction, which was found to be very common in real-world code. Some FPUs can also perform various transcendental functions such as exponential or trigonometric calculations, but the accuracy can be low, so some systems prefer to compute these functions in software. Floating-point operations were originally handled in software in early computers. Over time, manufacturers began to provide standardized floating-point libraries as part of their software collections. Some machines, those dedicated to scientific processing, would include specialized hardware to perform some of these tasks with much greater speed. The introduction of microcode in ...
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