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64-bit Floating-point
Double-precision floating-point format (sometimes called FP64 or float64) is a floating-point number format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 ''single precision'' and, more recently, base-10 representations (decimal floating point). One of the first programming languages to provide floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation and properties of floating-point data types depended on the computer manufacturer and computer model, and upon decisions made by programming-language implementers. E.g., GW-BASIC's double-precision dat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use Binary number, base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the correspond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signed Zero
Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are equivalent. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the '' sign-magnitude'' and ''ones' complement'' signed number representations for integers, and in most floating-point number representations. The number 0 is usually encoded as +0, but can still be represented by +0, −0, or 0. The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Real arithmetic with signed zeros can be considered a variant of the extended real number line such that = −∞ and = +∞; division ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single Precision
Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 231 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2−23) × 2127 ≈ 3.4028235 × 1038. All integers with seven or fewer decimal digits, and any 2''n'' for a whole number −149 ≤ ''n'' ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value. In the IEEE 754 standard, the 32-bit base-2 format is officially referred to as binary32; it was called single in IEEE 754-1985. IEEE 754 specifies additional floating-point types, such as 64-bit base-2 ''doubl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PA-RISC
Precision Architecture reduced instruction set computer, RISC (PA-RISC) or Hewlett Packard Precision Architecture (HP/PA or simply HPPA), is a computer, general purpose computer instruction set architecture (ISA) developed by Hewlett-Packard from the 1980s until the 2000s. The architecture was introduced on 26 February 1986, when the HP 3000, HP 3000 Series 930 and HP 9000, HP 9000 Model 840 computers were launched featuring the first implementation, the TS1. HP stopped selling PA-RISC-based HP 9000 systems at the end of 2008 but supported servers running PA-RISC chips until 2013. PA-RISC was succeeded by the Itanium (originally IA-64) ISA, jointly developed by HP and Intel. History In the late 1980s, HP was building four series of computers, all based on Complex instruction set computer, CISC CPUs. One line was the IBM PC compatible Intel i286-based Vectra Series, started in 1986. All others were non-Intel systems. One of them was the HP Series 300 of Motorola 68000-based wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ARM Architecture
ARM (stylised in lowercase as arm, formerly an acronym for Advanced RISC Machines and originally Acorn RISC Machine) is a family of reduced instruction set computer, RISC instruction set architectures (ISAs) for central processing unit, computer processors. Arm Holdings develops the ISAs and licenses them to other companies, who build the physical devices that use the instruction set. It also designs and licenses semiconductor intellectual property core, cores that implement these ISAs. Due to their low costs, low power consumption, and low heat generation, ARM processors are useful for light, portable, battery-powered devices, including smartphones, laptops, and tablet computers, as well as embedded systems. However, ARM processors are also used for desktop computer, desktops and server (computing), servers, including Fugaku (supercomputer), Fugaku, the world's fastest supercomputer from 2020 to 2022. With over 230 billion ARM chips produced, , ARM is the most widely used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE Floating Point
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 for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is something which is boundless, endless, or larger than any natural number. It is denoted by \infty, called the infinity symbol. From the time of the Ancient Greek mathematics, ancient Greeks, the Infinity (philosophy), philosophical nature of infinity has been the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including Guillaume de l'Hôpital, l'Hôpital and Johann Bernoulli, Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or Magnitude (mathematics), magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Number (computing)
In computing, a normal number is a non-zero number in a floating-point representation which is within the balanced range supported by a given floating-point format: it is a floating point number that can be represented without leading zeros in its significand. The magnitude of the smallest normal number in a format is given by: b^ where ''b'' is the base (radix) of the format (like common values 2 or 10, for binary and decimal number systems), and ''E_'' depends on the size and layout of the format. Similarly, the magnitude of the largest normal number in a format is given by :b^\cdot\left(b - b^\right) where ''p'' is the precision of the format in digits and ''E_'' is related to ''E_'' as: E_\, \overset\, 1 - E_ = \left(-E_\right) + 1 In the IEEE 754 binary and decimal formats, ''b'', ''p'', E_, and ''E_'' have the following values: For example, in the smallest decimal format in the table (decimal32), the range of positive normal numbers is 10−95 through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Offset-binary
Offset binary, also referred to as excess-K, excess-''N'', excess-e, excess code or biased representation, is a method for signed number representation where a signed number n is represented by the bit pattern corresponding to the unsigned number n+K, K being the ''biasing value'' or ''offset''. There is no standard for offset binary, but most often the ''K'' for an ''n''-bit binary word is ''K'' = 2''n''−1 (for example, the offset for a four-digit binary number would be 23=8). This has the consequence that the minimal negative value is represented by all-zeros, the "zero" value is represented by a 1 in the most significant bit and zero in all other bits, and the Integer overflow, maximal positive value is represented by all-ones (conveniently, this is the same as using two's complement but with the most significant bit inverted). It also has the consequence that in a logical comparison operation, one gets the same result as with a true form numerical comparison operat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Epsilon
Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point number systems. This value characterizes computer arithmetic in the field of numerical analysis, and by extension in the subject of computational science. The quantity is also called macheps and it has the symbols Greek epsilon \varepsilon. There are two prevailing definitions, denoted here as ''rounding machine epsilon'' or the ''formal definition'' and ''interval machine epsilon'' or ''mainstream definition''. In the ''mainstream definition'', machine epsilon is independent of rounding method, and is defined simply as ''the difference between 1 and the next larger floating point number''. In the ''formal definition'', machine epsilon is dependent on the type of rounding used and is also called unit roundoff, which has the symbol bold Roman u. The two terms can generally be considered to differ by simply a factor of two, with the ''formal definition'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 754 Double Floating Point Format
The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE has a corporate office in New York City and an operations center in Piscataway, New Jersey. The IEEE was formed in 1963 as an amalgamation of the American Institute of Electrical Engineers and the Institute of Radio Engineers. History The IEEE traces its founding to 1884 and the American Institute of Electrical Engineers. In 1912, the rival Institute of Radio Engineers was formed. Although the AIEE was initially larger, the IRE attracted more students and was larger by the mid-1950s. The AIEE and IRE merged in 1963. The IEEE is headquartered in New York City, but most business is done at the IEEE Operations Center in Piscataway, New Jersey, opened in 1975. The Australian Section of the IEEE existed between 1972 and 1985, after which it split into state- and te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
