| Floating-point formats |
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| IEEE 754 |
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| Other |
| Alternatives |
TensorFloat-32 or TF32 is a numeric floating point format designed for Tensor Core running on certain Nvidia GPUs.
The binary format is:
The total 19 bits fits within a double word (32 bits), and while it lacks precision compared with a normal 32 bit IEEE 754 floating point number, provides much faster computation, up to 8 times on a V100. [1]
In computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision:
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is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019.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.
SPARC is a reduced instruction set computer (RISC) instruction set architecture originally developed by Sun Microsystems. Its design was strongly influenced by the experimental Berkeley RISC system developed in the early 1980s. First developed in 1986 and released in 1987, SPARC was one of the most successful early commercial RISC systems, and its success led to the introduction of similar RISC designs from many vendors through the 1980s and 1990s.
In computing, NaN, standing for Not a Number, is a particular value of a numeric data type which is undefined as a number, such as the result of 0/0. Systematic use of NaNs was introduced by the IEEE 754 floating-point standard in 1985, along with the representation of other non-finite quantities such as infinities.
Double-precision floating-point format 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.
The IEEE Standard for Floating-Point Arithmetic 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 significand is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. Depending on the interpretation of the exponent, the significand may represent an integer or a fractional number.
Hexadecimal floating point is a format for encoding floating-point numbers first introduced on the IBM System/360 computers, and supported on subsequent machines based on that architecture, as well as machines which were intended to be application-compatible with System/360.
strictfp is an obsolete and redundant reserved word in the Java programming language. Previously, this keyword was used as a modifier that restricted floating-point calculations to IEEE 754 semantics to ensure portability. The strictfp keyword was introduced into Java with the Java virtual machine (JVM) version 1.2 and its functionality was removed in JVM version 17. As of Java 17, IEEE 754 semantics is required, thus using this keyword has no effect.
In C and related programming languages, long double refers to a floating-point data type that is often more precise than double precision though the language standard only requires it to be at least as precise as double. As with C's other floating-point types, it may not necessarily map to an IEEE format.
In computing, minifloats are floating-point values represented with very few bits. Predictably, they are not well suited for general-purpose numerical calculations. They are used for special purposes, most often in computer graphics, where iterations are small and precision has aesthetic effects. Machine learning also uses similar formats like bfloat16. Additionally, they are frequently encountered as a pedagogical tool in computer-science courses to demonstrate the properties and structures of floating-point arithmetic and IEEE 754 numbers.
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.
IEEE 754-2008 is a revision of the IEEE 754 standard for floating-point arithmetic. It was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 standard. The 2008 revision extended the previous standard where it was necessary, added decimal arithmetic and formats, tightened up certain areas of the original standard which were left undefined, and merged in IEEE 854 . In a few cases, where stricter definitions of binary floating-point arithmetic might be performance-incompatible with some existing implementation, they were made optional. In 2019, it was updated with a minor revision IEEE 754-2019.
In computing, half precision is a binary floating-point computer number format that occupies 16 bits 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.
In computing, quadruple precision is a binary floating-point–based computer number format that occupies 16 bytes with precision at least twice the 53-bit double precision.
Single-precision floating-point format 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.
In computing, Microsoft Binary Format (MBF) is a format for floating-point numbers which was used in Microsoft's BASIC languages, including MBASIC, GW-BASIC and QuickBASIC prior to version 4.00.
Fermi is the codename for a graphics processing unit (GPU) microarchitecture developed by Nvidia, first released to retail in April 2010, as the successor to the Tesla microarchitecture. It was the primary microarchitecture used in the GeForce 400 series and 500 series. All desktop Fermi GPUs were manufactured in 40nm, mobile Fermi GPUs in 40nm and 28nm. Fermi is the oldest microarchitecture from Nvidia that receives support for Microsoft's rendering API Direct3D 12 feature_level 11.
In computing, octuple precision is a binary floating-point-based computer number format that occupies 32 bytes in computer memory. This 256-bit octuple precision is for applications requiring results in higher than quadruple precision. This format is rarely used and very few environments support it.
The bfloat16 floating-point format is a computer number format occupying 16 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. This format is a shortened (16-bit) version of the 32-bit IEEE 754 single-precision floating-point format (binary32) with the intent of accelerating machine learning and near-sensor computing. It preserves the approximate dynamic range of 32-bit floating-point numbers by retaining 8 exponent bits, but supports only an 8-bit precision rather than the 24-bit significand of the binary32 format. More so than single-precision 32-bit floating-point numbers, bfloat16 numbers are unsuitable for integer calculations, but this is not their intended use. Bfloat16 is used to reduce the storage requirements and increase the calculation speed of machine learning algorithms.
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