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:
The Intel 386, originally released as 80386 and later renamed i386, is a 32-bit microprocessor introduced in 1985. The first versions had 275,000 transistors and were the CPU of many workstations and high-end personal computers of the time. As the original implementation of the 32-bit extension of the 80286 architecture, the i386 instruction set, programming model, and binary encodings are still the common denominator for all 32-bit x86 processors, which is termed the i386 architecture, x86, or IA-32, depending on context.
IEEE 754-1985 was an industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019.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.
x86 is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel based on the Intel 8086 microprocessor and its 8088 variant. The 8086 was introduced in 1978 as a fully 16-bit extension of Intel's 8-bit 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 processors.
A floating-point unit 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. Some FPUs can also perform various transcendental functions such as exponential or trigonometric calculations, but the accuracy can be very low, so that some systems prefer to compute these functions in software.
MMX is a single instruction, multiple data (SIMD) instruction set architecture designed by Intel, introduced on January 8, 1997 with its Pentium P5 (microarchitecture) based line of microprocessors, named "Pentium with MMX Technology". It developed out of a similar unit introduced on the Intel i860, and earlier the Intel i750 video pixel processor. MMX is a processor supplementary capability that is supported on IA-32 processors by Intel and other vendors as of 1997.
The Intel i860 is a RISC microprocessor design introduced by Intel in 1989. It is one of Intel's first attempts at an entirely new, high-end instruction set architecture since the failed Intel iAPX 432 from the beginning of the 1980s. It was the world's first million-transistor chip. It was released with considerable fanfare, slightly obscuring the earlier Intel i960, which was successful in some niches of embedded systems. The i860 never achieved commercial success and the project was terminated in the mid-1990s.
A coprocessor is a computer processor used to supplement the functions of the primary processor. 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.
The Am386 CPU is a 100%-compatible clone of the Intel 80386 design released by AMD in March 1991. It sold millions of units, positioning AMD as a legitimate competitor to Intel, rather than being merely a second source for x86 CPUs.
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents. More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g. a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation.
The Atari Microsoft BASIC and Atari Microsoft BASIC II variants of the 6502-version of Microsoft BASIC ported to the Atari 8-bit machines. The first version, released 1981, required 32 KB of RAM and was supplied on floppy disk. The second version, released the next year, had most of the code on a ROM cartridge with additional functions on an optional floppy.
Weitek Corporation was an American chip-design company that originally focused on floating-point units for a number of commercial CPU designs. During the early to mid-1980s, Weitek designs could be found powering a number of high-end designs and parallel-processing supercomputers.
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision.
The Intel 8087, announced in 1980, was the first x87 floating-point coprocessor for the 8086 line of microprocessors.
Hauppauge Computer Works is a US manufacturer and marketer of electronic video hardware for personal computers. Although it is most widely known for its WinTV line of TV tuner cards for PCs, Hauppauge also produces personal video recorders, digital video editors, digital media players, hybrid video recorders and digital television products for both Windows and Mac. The company is named after the hamlet of Hauppauge, New York, in which it is based.
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. 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.
The Intel 80387SX is the math coprocessor, also called an FPU, for the Intel 80386SX microprocessor. Introduced in 1987, it was used to perform floating-point arithmetic operations directly in hardware. The coprocessor was designed only to work with the 386SX, rather than the standard 386DX. This was because the original 80387 could not communicate with the altered 16 bit data bus of the 386SX, which was modified from the original 386DX's 32 bit data bus. The 387SX uses a 68-pin PLCC socket, just like some variants of the 80286 and the less common 80186 CPU, and was made in speeds ranging from 16 MHz to 33 MHz, matching the clock speed range of the Intel manufactured 386SX. Some chips like the IIT 3C87SX could get up to 40 MHz, matching the clock speeds of the fastest 386SX CPUs.
During the late 1980s, Intel sold two ISA expansion cards named Intel Inboard 386/AT and Intel Inboard 386/PC, which allowed users to upgrade an IBM AT or an IBM PC respectively. The boards allowed users to upgrade their machines' CPU to a 16 MHz 80386 processor. Both variants utilized a ribbon cable which plugged into the computer's original CPU socket on one end and into a socket on the Inboard card on the other end.
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 using special software.
Fractal-generating software is any type of graphics software that generates images of fractals. There are many fractal generating programs available, both free and commercial. Mobile apps are available to play or tinker with fractals. Some programmers create fractal software for themselves because of the novelty and because of the challenge in understanding the related mathematics. The generation of fractals has led to some very large problems for pure mathematics.
