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IEEE 754
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic 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 formats * ''e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal32 Floating-point Format
In computing, decimal32 is a decimal floating-point computer numbering format that occupies 4 bytes (32 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Like the binary16 format, it is intended for memory saving storage. Decimal32 supports 7 decimal digits of significand and an exponent range of −95 to +96, i.e. to ±. (Equivalently, to .) Because the significand is not normalized (there is no implicit leading "1"), most values with less than 7 significant digits have multiple possible representations; , etc. Zero has 192 possible representations (384 when both signed zeros are included). Decimal32 floating point is a relatively new decimal floating-point format, formally introduced in the 2008 version of IEEE 754 as well as with ISO/IEC/IEEE 60559:2011. Representation of decimal32 values IEEE 754 allows two alternative representation methods for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Organization For Standardization
The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Article 3 of the ISO Statutes. ISO was founded on 23 February 1947, and (as of November 2022) it has published over 24,500 international standards covering almost all aspects of technology and manufacturing. It has 809 Technical committees and sub committees to take care of standards development. The organization develops and publishes standardization in all technical and nontechnical fields other than Electrical engineering, electrical and electronic engineering, which is handled by the International Electrotechnical Commission, IEC.Editors of Encyclopedia Britannica. 3 June 2021.International Organization for Standardization" ''Encyclopedia Britannica''. Retrieved 2022-04-26. It is headquartered in Geneva, Switzerland, and works in 167 coun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octuple-precision Floating-point Format
In computing, octuple precision is a binary floating-point-based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256-bit octuple precision is for applications requiring results in higher than quadruple precision. This format is rarely (if ever) used and very few environments support it. IEEE 754 octuple-precision binary floating-point format: binary256 In its 2008 revision, the IEEE 754 standard specifies a binary256 format among the ''interchange formats'' (it is not a basic format), as having: * Sign bit: 1 bit * Exponent width: 19 bits * Significand precision: 237 bits (236 explicitly stored) The format is written with an implicit lead bit with value 1 unless the exponent is all zeros. Thus only 236 bits of the significand appear in the memory format, but the total precision is 237 bits (approximately 71 decimal digits: ). The bits are laid out as follows: Exponent encoding The octuple-precision binary floating-point exponent is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadruple-precision Floating-point Format
In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision. This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision, but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables. William Kahan, primary architect of the original IEEE-754 floating point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double-precision Floating-point Format
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 dynamic range of numeric values by using a floating radix point. Floating point is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754-2008 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. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-precision Floating-point Format
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 7 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 754-2008 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 '' double ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Half-precision Floating-point Format
In computing, half precision (sometimes called FP16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks. Almost all modern uses follow the IEEE 754-2008 standard, where the 16-bit base-2 format is referred to as binary16, and the exponent uses 5 bits. This can express values in the range ±65,504, with the minimum value above 1 being 1 + 1/1024. Depending on the computer, half-precision can be over an order of magnitude faster than double precision, e.g. 550 PFLOPS for half-precision vs 37 PFLOPS for double precision on one cloud provider. History Several earlier 16-bit floating point formats have existed including that of Hitachi's HD61810 DSP of 1982, Scott's WIF and the 3dfx Voodoo Graphics processor. ILM was searching for an image fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interchange Formats
Interchange may refer to: Transport * Interchange (road), a collection of ramps, exits, and entrances between two or more highways * Interchange (freight rail), the transfer of freight cars between railroad companies * Interchange station, a railway station where two or more routes meet and allow passengers to change trains * Cross-platform interchange, the transfer between trains across a station platform * Transport interchange or transport hub to include jointly operated interchange flights by two or more airlines Other uses * ''Interchange'' (de Kooning), a 1955 painting by Willem de Kooning * ''Interchange'' (album), a 1994 album by guitarist Pat Martino * Interchange (Australian rules football), a team position in Australian rules football * Interchange circuit, a circuit that facilitates the exchange of data and signaling information * Interchange fee, a fee paid between banks in the payment card industry * ''Interchange'' (film), a 2016 Malaysian fantasy thriller f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary64
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 dynamic range of numeric values by using a floating radix point. Floating point is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754-2008 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. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran. Before the widespread adoption of IEEE 754-1985, the representation an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary32
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 7 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 754-2008 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 '' double ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitHub
GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, it has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. As of June 2022, GitHub reported having over 83 million developers and more than 200 million repositories, including at least 28 million public repositories. It is the largest source code host . History GitHub.com Development of the GitHub.com platform began on October 19, 2007. The site was launched in April 2008 by Tom Preston-Werner, Chris Wanstrath, P. J. Hyett and Scott Chacon after it had been made available for a few months prior as a beta release. GitHub has an annual keynote called GitHub Universe. Organizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponent Bias
In IEEE 754 floating-point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias, also called a biased exponent. Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement, the usual representation for signed values, would make comparison harder. To solve this problem the exponent is stored as an unsigned value which is suitable for comparison, and when being interpreted it is converted into an exponent within a signed range by subtracting the bias. By arranging the fields such that the sign bit takes the most significant bit position, the biased exponent takes the middle position, then the significand will be the least significant bits and the resulting value will be ordered properly. This is the case whether or not it is interpreted as a floating-point or integer value. The purpose of this is to enable high spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
