Saturation Arithmetic
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Saturation Arithmetic
Saturation arithmetic is a version of arithmetic in which all operations, such as addition and multiplication, are limited to a fixed range between a minimum and maximum value. If the result of an operation is greater than the maximum, it is set (" clamped") to the maximum; if it is below the minimum, it is clamped to the minimum. The name comes from how the value becomes "saturated" once it reaches the extreme values; further additions to a maximum or subtractions from a minimum will not change the result. For example, if the valid range of values is from −100 to 100, the following ''saturating arithmetic operations'' produce the following values: *60 + 30 → 90. *60 + 43 → 100. (''not'' the expected 103.) *(60 + 43) − (75 + 25) → 0. (''not'' the expected 3.) (100 − 100 → 0.) *10 × 11 → 100. (''not'' the expected 110.) *99 × 99 → 100. (''not'' the expected 9801.) *30 × (5 − 1) → 100. (''not'' the expected 120.) (30 × 4 → 100.) *(30 × 5) − (30 × 1) � ...
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Arithmetic
Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the ...
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AVX2
Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge New Instructions) are SIMD extensions to the x86 instruction set architecture for microprocessors from Intel and Advanced Micro Devices (AMD). They were proposed by Intel in March 2008 and first supported by Intel with the Sandy Bridge microarchitecture shipping in Q1 2011 and later by AMD with the Bulldozer microarchitecture shipping in Q4 2011. AVX provides new features, new instructions, and a new coding scheme. AVX2 (also known as Haswell New Instructions) expands most integer commands to 256 bits and introduces new instructions. They were first supported by Intel with the Haswell microarchitecture, which shipped in 2013. AVX-512 expands AVX to 512-bit support using a new EVEX prefix encoding proposed by Intel in July 2013 and first supported by Intel with the Knights Landing co-processor, which shipped in 2016. In conventional processors, AVX-512 was introduced with Skylak ...
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IBM 704
The IBM 704 is the model name of a large digital computer, digital mainframe computer introduced by IBM in 1954. Designed by John Backus and Gene Amdahl, it was the first mass-produced computer with hardware for floating-point arithmetic. The IBM 704 ''Manual of operation'' states: The type 704 Electronic Data-Processing Machine is a large-scale, high-speed electronic calculator controlled by an internally stored program of the single address type. The 704 at that time was thus regarded as "pretty much the only computer that could handle complex math". The 704 was a significant improvement over the earlier IBM 701 in terms of architecture and implementation. Like the 701, the 704 used vacuum-tube logic circuitry, but increased the instruction size from 18-bit computing, 18 bits to 36-bit computing, 36 bits, the same as the memory's word size. Changes from the 701 include the use of magnetic-core memory instead of Williams tubes, floating-point arithmetic instructions, 15 ...
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Real Numbers
In mathematics, a real number is a number that can be used to measurement, measure a continuous variable, continuous one-dimensional quantity such as a time, duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limit (mathematics), limits, continuous function, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally mathematical notation, denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction (mathematics), fraction . ...
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IEEE Floating-point Standard
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard. The standard defines: * ''arithmetic formats:'' sets of binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinities, and special "not a number" values ( NaNs) * ''interchange formats:'' encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form * ''rounding rules:'' properties to be satisfied when rounding numbers during arithmetic and conversions * ''operations:'' arithmetic and other operations (such as trigonometric functions) on arithmetic format ...
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Conditional Move
In computer architecture, predication is a feature that provides an alternative to Conditional (computer programming), conditional transfer of control flow, control, as implemented by conditional branch (computer science), branch machine instruction (computer science), instructions. Predication works by having conditional (''predicated'') non-branch instructions associated with a ''predicate'', a Boolean data type, Boolean value used by the instruction to control whether the instruction is allowed to modify the architectural state or not. If the predicate specified in the instruction is true, the instruction modifies the architectural state; otherwise, the architectural state is unchanged. For example, a predicated move instruction (a conditional move) will only modify the destination if the predicate is true. Thus, instead of using a conditional branch to select an instruction or a sequence of instructions to Execution (computing), execute based on the predicate that controls ...
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Zilog Z80
The Zilog Z80 is an 8-bit computing, 8-bit microprocessor designed by Zilog that played an important role in the evolution of early personal computing. Launched in 1976, it was designed to be Backward compatibility, software-compatible with the Intel 8080, offering a compelling alternative due to its better Integrated circuit, integration and increased performance. Along with the 8080's seven Processor register, registers and flags register, the Z80 introduced an alternate register set, two 16-bit index registers, and additional instructions, including bit manipulation and block copy/search. Originally intended for use in embedded systems like the 8080, the Z80's combination of compatibility, affordability, and superior performance led to widespread adoption in video game systems and home computers throughout the late 1970s and early 1980s, helping to fuel the personal computing revolution. The Z80 was used in iconic products such as the Osborne 1, TRS-80, Radio Shack TRS-80, Col ...
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Intel 8086
The 8086 (also called iAPX 86) is a 16-bit computing, 16-bit microprocessor chip designed by Intel between early 1976 and June 8, 1978, when it was released. The Intel 8088, released July 1, 1979, is a slightly modified chip with an external 8-bit Bus (computing), data bus (allowing the use of cheaper and fewer supporting Integrated circuit, ICs),Fewer TTL buffers, latches, multiplexers (although the amount of TTL logic was not drastically reduced). It also permits the use of cheap 8080-family ICs, where the 8254 CTC, Intel 8255, 8255 PIO, and 8259 PIC were used in the IBM PC design. In addition, it makes PCB layout simpler and boards cheaper, as well as demanding fewer (1- or 4-bit wide) DRAM chips. and is notable as the processor used in the original IBM Personal Computer, IBM PC design. The 8086 gave rise to the x86 architecture, which eventually became Intel's most successful line of processors. On June 5, 2018, Intel released a limited-edition CPU celebrating the 40th anniv ...
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Branch (computer Science)
A branch, jump or transfer is an instruction in a computer program that can cause a computer to begin executing a different instruction sequence and thus deviate from its default behavior of executing instructions in order. ''Branch'' (or ''branching'', ''branched'') may also refer to the act of switching execution to a different instruction sequence as a result of executing a branch instruction. Branch instructions are used to implement control flow in program loops and conditionals (i.e., executing a particular sequence of instructions only if certain conditions are satisfied). A branch instruction can be either an ''unconditional branch'', which always results in branching, or a ''conditional branch'', which may or may not cause branching depending on some condition. Also, depending on how it specifies the address of the new instruction sequence (the "target" address), a branch instruction is generally classified as ''direct'', ''indirect'' or ''relative'', meaning that the ...
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C++26
C26 or C-26 may refer to: * C.26, a British World War I Coastal class airship * C26 road (Namibia) * Caldwell 26, a spiral galaxy * Caspar C 26, German sport plane * Douglas C-26 Dolphin, an American military flying boat * Fairchild C-26 Metroliner, an American military transport * , C-class submarine of the Royal Navy {{Letter-NumberCombDisambig ...
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Eiffel (programming Language)
Eiffel is an object-oriented programming language designed by Bertrand Meyer (an object-orientation proponent and author of '' Object-Oriented Software Construction'') and Eiffel Software. Meyer conceived the language in 1985 with the goal of increasing the reliability of commercial software development. The first version was released in 1986. In 2005, the International Organization for Standardization (ISO) released a technical standard for Eiffel. The design of the language is closely connected with the Eiffel programming method. Both are based on a set of principles, including design by contract, command–query separation, the uniform-access principle, the single-choice principle, the open–closed principle, and option–operand separation. Many concepts initially introduced by Eiffel were later added into Java, C#, and other languages. New language design ideas, particularly through the Ecma/ ISO standardization process, continue to be incorporated into the Eiffe ...
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LLVM
LLVM, also called LLVM Core, is a target-independent optimizer and code generator. It can be used to develop a Compiler#Front end, frontend for any programming language and a Compiler#Back end, backend for any instruction set architecture. LLVM is designed around a language-independent specification, language-independent intermediate representation (IR) that serves as a Software portability, portable, high-level assembly language that can be optimizing compiler, optimized with a variety of transformations over multiple passes. The name ''LLVM'' originally stood for ''Low Level Virtual Machine.'' However, the project has since expanded, and the name is no longer an acronym but an orphan initialism. LLVM is written in C++ and is designed for compile-time, Linker (computing), link-time, runtime (program lifecycle phase), runtime, and "idle-time" optimization. Originally implemented for C (programming language), C and C++, the language-agnostic design of LLVM has since spawned a wide ...
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