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X87
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 worked in tandem with corresponding x86 CPUs. These microchips had names ending in "87". This was 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 ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point
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-p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intel P5 (microarchitecture)
The Pentium (also referred to as P5, its microarchitecture, or i586) is a fifth generation, 32-bit x86 microprocessor that was introduced by Intel on March 22, 1993, as the very first CPU in the Pentium brand. It was instruction set compatible with the 80486 but was a new and very different microarchitecture design from previous iterations. The P5 Pentium was the first superscalar x86 microarchitecture and the world's first superscalar microprocessor to be in mass productionmeaning it generally executes at least 2 instructions per clock mainly because of a design-first dual integer pipeline design previously thought impossible to implement on a CISC microarchitecture. Additional features include a faster floating-point unit, wider data bus, separate code and data caches, and many other techniques and features to enhance performance and support security, encryption, and multiprocessing, for workstations and servers when compared to the next best previous industry standard proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyrix 6x86
The Cyrix 6x86 is a line of sixth-generation, 32-bit x86 microprocessors designed and released by Cyrix in 1995. Cyrix, being a fabless company, had the chips manufactured by IBM and SGS-Thomson. The 6x86 was made as a direct competitor to Intel's Pentium microprocessor line, and was pin compatible. During the 6x86's development, the majority of applications ( office software as well as games) performed almost entirely integer operations. The designers foresaw that future applications would most likely maintain this instruction focus. So, to optimize the chip's performance for what they believed to be the most likely application of the CPU, the integer execution resources received most of the transistor budget. This would later prove to be a strategic mistake, as the popularity of the P5 Pentium caused many software developers to hand-optimize code in assembly language, to take advantage of the P5 Pentium's tightly pipelined and lower latency FPU. For example, the highly anti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
80486
The Intel 486, officially named i486 and also known as 80486, is a microprocessor. It is a higher-performance follow-up to the Intel 386. The i486 was introduced in 1989. 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. A typical 50 MHz i486 executes around 40 million instructions per second (MIPS), reaching 50 MIPS peak performance. It is approximately twice as fast as the i386 or i286 per clock cycle. The i486's improved performance is thanks to its five-stage pipeline with all stages bound to a single cycle. The enhanced FPU unit on the chip was significantly faster than the i387 FPU per cycle. The intel 80387 FPU ("i387") was a separate, optional math coprocessor that was installed in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second
The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of Units ( SI) is more precise:The second ..is defined by taking the fixed numerical value of the caesium frequency, Δ''ν''Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be when expressed in the unit Hz, which is equal to s−1. This current definition was adopted in 1967 when it became feasible to define the second based on fundamental properties of nature with caesium clocks. Because the speed of Earth's rotation varies and is slowing ever so slightly, a leap second is added at irregular intervals to civil time to keep clocks in sync with Earth's rotation. Uses Analog clocks and watches often ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Precision
Significant figures (also known as the significant digits, ''precision'' or ''resolution'') of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expressing the result of a measurement (e.g., length, pressure, volume, or mass) has more digits than the number of digits allowed by the measurement resolution, then only as many digits as allowed by the measurement resolution are reliable, and so only these can be significant figures. For example, if a length measurement gives 114.8 mm while the smallest interval between marks on the ruler used in the measurement is 1 mm, then the first three digits (1, 1, and 4, showing 114 mm) are certain and so they are significant figures. Digits which are uncertain but ''reliable'' are also considered significant figures. In this example, the last digit (8, which adds 0.8 mm) is also considered a significant figure even though the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significand
The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. Depending on the interpretation of the exponent, the significand may represent an integer or a fraction. Example The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10−2 power term, also called characteristics, where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic: : 123.45 = 12345 × 10−2. The same value can also be represented in normalized form with 1.2345 as the fractional coefficient, and +2 as the exponent (and 10 as the base): : 123.45 = 1.2345 × 10+2. Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form. For base 2, this 1.xxxx form is also called a normalize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
64-bit
In computer architecture, 64-bit integers, memory addresses, or other data units are those that are 64 bits wide. Also, 64-bit CPUs and ALUs are those that are based on processor registers, address buses, or data buses of that size. A computer that uses such a processor is a 64-bit computer. From the software perspective, 64-bit computing means the use of machine code with 64-bit virtual memory addresses. However, not all 64-bit instruction sets support full 64-bit virtual memory addresses; x86-64 and ARMv8, for example, support only 48 bits of virtual address, with the remaining 16 bits of the virtual address required to be all 0's or all 1's, and several 64-bit instruction sets support fewer than 64 bits of physical memory address. The term ''64-bit'' also describes a generation of computers in which 64-bit processors are the norm. 64 bits is a word size that defines certain classes of computer architecture, buses, memory, and CPUs and, by extension, the software that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Round-off Error
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 of roundoff e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SSE2
SSE2 (Streaming SIMD Extensions 2) is one of the Intel SIMD (Single Instruction, Multiple Data) processor supplementary instruction sets first introduced by Intel with the initial version of the Pentium 4 in 2000. It extends the earlier SSE instruction set, and is intended to fully replace MMX. Intel extended SSE2 to create SSE3 in 2004. SSE2 added 144 new instructions to SSE, which has 70 instructions. 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. Features Most of the SSE2 instructions implement the integer vector operations also found in MMX. Instead of the MMX registers they use the XMM registers, which are wider and allow for significant performance improvements in specialized applications. Another advantage of replacing MMX with SSE2 is avoiding the mode switching penalty for issuing x87 instructions present in MMX because it is sharing register space with the x87 FPU. The SSE2 als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating Point
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-poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
