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Half Precision Floating-point Format
In computing, half precision (sometimes called FP16 or float16) 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 (a 4-bit exponent and a 12-bit mantissa), Thomas J. Scott's WIF of 1991 (5 exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bfloat16 Floating-point Format
The bfloat16 (brain floating point) 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. The bfloat16 format was developed by Google Brain, an artificial intelligence research group at Google. It is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nvidia
Nvidia Corporation ( ) is an American multinational corporation and technology company headquartered in Santa Clara, California, and incorporated in Delaware. Founded in 1993 by Jensen Huang (president and CEO), Chris Malachowsky, and Curtis Priem, it designs and supplies graphics processing units (GPUs), application programming interfaces (APIs) for data science and high-performance computing, and system on a chip units (SoCs) for mobile computing and the automotive market. Nvidia is also a leading supplier of artificial intelligence (AI) hardware and software. Nvidia outsources the manufacturing of the hardware it designs. Nvidia's professional line of GPUs are used for edge-to-cloud computing and in supercomputers and workstations for applications in fields such as architecture, engineering and construction, media and entertainment, automotive, scientific research, and manufacturing design. Its GeForce line of GPUs are aimed at the consumer market and are used in ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit In The Last Place
In computer science and numerical analysis, unit in the last place or unit of least precision (ulp) is the spacing between two consecutive floating-point numbers, i.e., the value the '' least significant digit'' (rightmost digit) represents if it is 1. It is used as a measure of accuracy in numeric calculations. Definition The most common definition is: In radix b with precision p, if b^e \le , x, x. Otherwise, \operatorname (x + 1) = x or \operatorname (x + 1) = x + \operatorname(x), depending on the value of the least significant digit and the exponent of x. This is demonstrated in the following Haskell code typed at an interactive prompt: > until (\x -> x x+1) (+1) 0 :: Float 1.6777216e7 > it-1 1.6777215e7 > it+1 1.6777216e7 Here we start with 0 in single precision (binary32) and repeatedly add 1 until the operation does not change the value. Since the significand for a single-precision number contains 24 bits, the first integer that is not exactly representable is 224+ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significand
The significand (also coefficient, sometimes argument, or more ambiguously mantissa, fraction, or characteristic) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign. Depending on the interpretation of the exponent, the significand may represent an integer or a fractional number, which may cause the term "mantissa" to be misleading, since the ''mantissa'' of a logarithm is always its fractional part. Although the other names mentioned are common, ''significand'' is the word used by IEEE 754, an important technical standard for floating-point arithmetic. In mathematics, the term "argument" may also be ambiguous, since "the argument of a number" sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane. Example The number 123.45 can be represented as a decimal floati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 754r Half 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] |
Precision (arithmetic)
Significant figures, also referred to as significant digits, are specific digits within a number that is written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcome of a measurement (such as length, pressure, volume, or mass), if the number of digits exceeds what the measurement instrument can resolve, only the digits that are determined by the resolution are dependable and therefore considered significant. For instance, if a length measurement yields 114.8 mm, using a ruler with the smallest interval between marks at 1 mm, the first three digits (1, 1, and 4, representing 114 mm) are certain and constitute significant figures. Further, digits that are uncertain yet meaningful are also included in the significant figures. In this example, the last digit (8, contributing 0.8 mm) is likewise considered significant despite its uncertainty. Therefore, this measurement contains f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significand
The significand (also coefficient, sometimes argument, or more ambiguously mantissa, fraction, or characteristic) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign. Depending on the interpretation of the exponent, the significand may represent an integer or a fractional number, which may cause the term "mantissa" to be misleading, since the ''mantissa'' of a logarithm is always its fractional part. Although the other names mentioned are common, ''significand'' is the word used by IEEE 754, an important technical standard for floating-point arithmetic. In mathematics, the term "argument" may also be ambiguous, since "the argument of a number" sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane. Example The number 123.45 can be represented as a decimal floati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponent
In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_.In particular, b^1=b. The exponent is usually shown as a superscript to the right of the base as or in computer code as b^n. This binary operation is often read as " to the power "; it may also be referred to as " raised to the th power", "the th power of ", or, most briefly, " to the ". The above definition of b^n immediately implies several properties, in particular the multiplication rule:There are three common notations for multiplication: x\times y is most commonly used for explicit numbers and at a very elementary level; xy is most common when variables are used; x\cdot y is used for emphasizing that one talks of multiplication or when omitting the multiplication sign would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sign Bit
In computer science, the sign bit is a bit in a signed number representation that indicates the sign of a number. Although only signed numeric data types have a sign bit, it is invariably located in the most significant bit position, so the term may be used interchangeably with "most significant bit" in some contexts. Almost always, if the sign bit is 0, the number is non-negative (positive or zero). If the sign bit is 1 then the number is negative. Formats other than two's complement integers allow a signed zero: distinct "positive zero" and "negative zero" representations, the latter of which does not correspond to the mathematical concept of a negative number. When using a complement representation, to convert a signed number to a wider format the additional bits must be filled with copies of the sign bit in order to preserve its numerical value, a process called '' sign extension'' or ''sign propagation''. Sign bit weight in Two's complement Two's complement is by far th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F16C
The F16C (previously/informally known as CVT16) instruction set is an x86 instruction set architecture extension which provides support for converting between half-precision and standard IEEE single-precision floating-point formats. History The CVT16 instruction set, announced by AMD on May 1, 2009, is an extension to the 128-bit SSE core instructions in the x86 and AMD64 instruction sets. CVT16 is a revision of part of the SSE5 instruction set proposal announced on August 30, 2007, which is supplemented by the XOP and FMA4 instruction sets. This revision makes the binary coding of the proposed new instructions more compatible with Intel's AVX instruction extensions, while the functionality of the instructions is unchanged. In recent documents, the name F16C is formally used in both Intel and AMD x86-64 architecture specifications. Technical information There are variants that convert four floating-point values in an XMM register or 8 floating-point values in a YMM re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tegra
Tegra is a system on a chip (SoC) series developed by Nvidia for mobile devices such as smartphones, personal digital assistants, and mobile Internet devices. The Tegra integrates an ARM architecture central processing unit (CPU), graphics processing unit (GPU), northbridge, southbridge, and memory controller onto one package. Early Tegra SoCs are designed as efficient multimedia processors. The Tegra-line evolved to emphasize performance for gaming and machine learning applications without sacrificing power efficiency, before taking a drastic shift in direction towards platforms that provide vehicular automation with the applied "Nvidia Drive" brand name on reference boards and its semiconductors; and with the " Nvidia Jetson" brand name for boards adequate for AI applications within e.g. robots or drones, and for various smart high level automation purposes. History The Tegra APX 2500 was announced on February 12, 2008. The Tegra 6xx product line was revealed on June 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GeForce FX
The GeForce FX or "GeForce 5" series (codenamed NV30) is a line of graphics processing units from the manufacturer Nvidia. Overview Nvidia's GeForce FX series is the fifth generation of the GeForce line. With GeForce 3, the company introduced programmable shader functionality into their 3D architecture, in line with the release of Microsoft's DirectX 8.0. The GeForce 4 Ti was an enhancement of the GeForce 3 technology. With real-time 3D graphics technology continually advancing, the release of DirectX 9.0 brought further refinement of programmable pipeline technology with the arrival of Shader Model 2.0. The GeForce FX series is Nvidia's first generation Direct3D 9-compliant hardware. The series was manufactured on TSMC's 130 nm fabrication process. It is compliant with Shader Model 2.0/2.0A, allowing more flexibility in complex shader/fragment programs and much higher arithmetic precision. It supports a number of new memory technologies, including DDR2, GDDR2 and GDDR3 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
