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80387
x87 is a floating-point-related subset of the x86 architecture instruction set. It originated as an extension of the 8086 instruction set in the form of optional floating-point coprocessors that work in tandem with corresponding x86 CPUs. These microchips have names ending in "87". This is also known as the NPX (numeric processor extension). Like other extensions to the basic instruction set, x87 instructions are not strictly needed to construct working programs, but provide hardware and microcode implementations of common numerical tasks, allowing these tasks to be performed much faster than corresponding machine code routines can. The x87 instruction set includes instructions for basic floating-point operations such as addition, subtraction and comparison, but also for more complex numerical operations, such as the computation of the tangent function and its inverse, for example. Most x86 processors since the Intel 80486 have had these x87 instructions implemented in the main CP ...
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Extended Precision
Extended precision refers to floating-point number formats that provide greater precision than the basic floating-point formats. Extended-precision formats support a basic format by minimizing roundoff and overflow errors in intermediate values of expressions on the base format. In contrast to ''extended precision'', arbitrary-precision arithmetic refers to implementations of much larger numeric types (with a storage count that usually is not a power of two) using special software (or, rarely, hardware). Extended-precision implementations There is a long history of extended floating-point formats reaching back nearly to the middle of the last century.. Various manufacturers have used different formats for extended precision for different machines. In many cases the format of the extended precision is not quite the same as a scale-up of the ordinary single- and double-precision formats it is meant to extend. In a few cases the implementation was merely a software-based change i ...
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X86 Architecture
x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel, based on the 8086 microprocessor and its 8-bit-external-bus variant, the 8088. The 8086 was introduced in 1978 as a fully 16-bit extension of 8-bit Intel's 8080 microprocessor, with memory segmentation as a solution for addressing more memory than can be covered by a plain 16-bit address. The term "x86" came into being because the names of several successors to Intel's 8086 processor end in "86", including the 80186, 80286, 80386 and 80486. Colloquially, their names were "186", "286", "386" and "486". The term is not synonymous with IBM PC compatibility, as this implies a multitude of other computer hardware. Embedded systems and general-purpose computers used x86 chips before the PC-compatible market started, some of them before the IBM PC (1981) debut. , most desktop and laptop computers sold are based o ...
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Coprocessor
A coprocessor is a computer processor used to supplement the functions of the primary processor (the CPU). Operations performed by the coprocessor may be floating-point arithmetic, graphics, signal processing, string processing, cryptography or I/O interfacing with peripheral devices. By offloading processor-intensive tasks from the main processor, coprocessors can accelerate system performance. Coprocessors allow a line of computers to be customized, so that customers who do not need the extra performance do not need to pay for it. Functionality Coprocessors vary in their degree of autonomy. Some (such as FPUs) rely on direct control via coprocessor instructions, embedded in the CPU's instruction stream. Others are independent processors in their own right, capable of working asynchronously; they are still not optimized for general-purpose code, or they are incapable of it due to a limited instruction set focused on accelerating specific tasks. It is common for these to b ...
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80486
The Intel 486, officially named i486 and also known as 80486, is a microprocessor introduced in 1989. It is a higher-performance follow-up to the Intel 386. It represents the fourth generation of binary compatible CPUs following the 8086 of 1978, the Intel 80286 of 1982, and 1985's i386. It was the first tightly- pipelined x86 design as well as the first x86 chip to include more than one million transistors. It offered a large on-chip cache and an integrated floating-point unit. When it was announced, the initial performance was originally published between 15 and 20 VAX MIPS, between 37,000 and 49,000 dhrystones per second, and between 6.1 and 8.2 double-precision megawhetstones per second for both 25 and 33 MHz version. A typical 50 MHz i486 executes 41 million instructions per second Dhrystone MIPS and SPEC integer rating of 27.9.Chen, Allan, "The 50-MHz Intel486 Microprocessor", Intel Corporation, Microcomputer Solutions, September/October 1991, page 2. ...
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Intel 80486
The Intel 486, officially named i486 and also known as 80486, is a microprocessor introduced in 1989. It is a higher-performance follow-up to the i386, Intel 386. It represents the fourth generation of binary compatible CPUs following the Intel 8086, 8086 of 1978, the Intel 80286 of 1982, and 1985's i386. It was the first tightly-instruction pipeline, pipelined x86 design as well as the first x86 chip to include more than one million transistors. It offered a large on-chip Cache (computing), cache and an integrated floating-point unit. When it was announced, the initial performance was originally published between 15 and 20 VAX Unit of Performance, VAX MIPS, between 37,000 and 49,000 Dhrystone, dhrystones per second, and between 6.1 and 8.2 double-precision Whetstone (benchmark), megawhetstones per second for both 25 and 33 MHz version. A typical 50 MHz i486 executes 41 million instructions per second Dhrystone MIPS and SPECint, SPEC integer rating of 27.9.Chen, ...
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8086
The 8086 (also called iAPX 86) is a 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 data bus (allowing the use of cheaper and fewer supporting 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, 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 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 anniversary of the Intel 8086, called the Intel Core i7-8086K. History Background In 1972 ...
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Binary Function
In mathematics, a binary function (also called bivariate function, or function of two variables) is a function that takes two inputs. Precisely stated, a function f is binary if there exists sets X, Y, Z such that :\,f \colon X \times Y \rightarrow Z where X \times Y is the Cartesian product of X and Y. Alternative definitions Set-theoretically, a binary function can be represented as a subset of the Cartesian product X \times Y \times Z, where (x,y,z) belongs to the subset if and only if f(x,y) = z. Conversely, a subset R defines a binary function if and only if for any x \in X and y \in Y, there exists a unique z \in Z such that (x,y,z) belongs to R. f(x,y) is then defined to be this z. Alternatively, a binary function may be interpreted as simply a function from X \times Y to Z. Even when thought of this way, however, one generally writes f(x,y) instead of f((x,y)). (That is, the same pair of parentheses is used to indicate both function application and the formation ...
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ACM Transactions On Programming Languages And Systems
The ''ACM Transactions on Programming Languages and Systems'' (''TOPLAS'') is a bimonthly, open access, peer-reviewed scientific journal on the topic of programming languages published by the Association for Computing Machinery. Background Published since 1979, the journal's scope includes programming language design, implementation, and semantics of programming languages, compilers and interpreters, run-time systems, storage allocation and garbage collection, and formal specification, testing, and verification of software. It is indexed in Scopus and SCImago. The editor-in-chief is Andrew Myers (Cornell University). According to the ''Journal Citation Reports'', the journal had a 2020 impact factor of 0.410. References External links * TOPLASat ACM Digital Library TOPLASat DBLP DBLP is a computer science bibliography website. Starting in 1993 at Universität Trier in Germany, it grew from a small collection of HTML files and became an organization hosting a datab ...
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IEEE 754-1985
IEEE 754-1985 is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. During its 23 years, it was the most widely used format for floating-point computation. It was implemented in software, in the form of floating-point libraries, and in hardware, in the instructions of many CPUs and FPUs. The first integrated circuit to implement the draft of what was to become IEEE 754-1985 was the Intel 8087. IEEE 754-1985 represents numbers in binary, providing definitions for four levels of precision, of which the two most commonly used are: The standard also defines representations for positive and negative infinity, a "negative zero", five exceptions to handle invalid results like division by zero, special values called NaNs for representing those exceptions, denormal numbers to represent numbers smaller than shown above, a ...
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IEEE 754
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 #Design rationale, addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and Software portability, portably. Many hardware floating-point units use the IEEE 754 standard. The standard defines: * ''arithmetic formats:'' sets of Binary code, binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinity, 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 operatio ...
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Round-off Error
In computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. Rounding errors are due to inexactness in the representation of real numbers and the arithmetic operations done with them. This is a form of quantization error. When using approximation equations or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits), one of the goals of numerical analysis is to estimate computation errors. Computation errors, also called numerical errors, include both truncation errors and roundoff errors. When a sequence of calculations with an input involving any roundoff error are made, errors may accumulate, sometimes dominating the calculation. In ill-conditioned problems, significant error may accumulate. In short, there are two major facets ...
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SSE2
SSE2 (Streaming SIMD Extensions 2) is one of the Intel SIMD (Single Instruction, Multiple Data) processor supplementary instruction sets introduced by Intel with the initial version of the Pentium 4 in 2000. SSE2 instructions allow the use of XMM (SIMD) registers on x86 instruction set architecture processors. These registers can load up to 128 bits of data and perform instructions, such as vector addition and multiplication, simultaneously. SSE2 introduced double-precision floating point instructions in addition to the single-precision floating point and integer instructions found in SSE. SSE2 extends earlier SSE instruction set by adding 144 new instructions to the previous 70 instructions. SSE2 intends to fully replace MMX, a SIMD instruction set found on IA-32 architecture processors. Competing chip-maker AMD added support for SSE2 with the introduction of their Opteron and Athlon 64 ranges of AMD64 64-bit CPUs in 2003. SSE2 was extended to create SSE3 in 2004, and e ...
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