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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 truncated (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. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Half-precision Floating-point Format
In computing, half precision (sometimes called FP16) is a binary (computing), 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 radix, 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 Interactive, 3dfx Voodoo Graphics proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
FPGA
A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturinghence the term '' field-programmable''. The FPGA configuration is generally specified using a hardware description language (HDL), similar to that used for an application-specific integrated circuit (ASIC). Circuit diagrams were previously used to specify the configuration, but this is increasingly rare due to the advent of electronic design automation tools. FPGAs contain an array of programmable logic blocks, and a hierarchy of reconfigurable interconnects allowing blocks to be wired together. Logic blocks can be configured to perform complex combinational functions, or act as simple logic gates like AND and XOR. In most FPGAs, logic blocks also include memory elements, which may be simple flip-flops or more complete blocks of memory. Many FPGAs can be reprogrammed to implement different logic functions, allowing flexible reconfigurabl ... [...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, although 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. In the two's complement representation, the sign bit has the weight where is the number of bits. In the ones' complement representation, the most negative value is , but there are two representations of zero, one for each value of the sign bit. In a sign-and-magnitude representation of numbers, the value o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 * ''excepti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Conversion
In computer science, type conversion, type casting, type coercion, and type juggling are different ways of changing an expression from one data type to another. An example would be the conversion of an integer value into a floating point value or its textual representation as a string, and vice versa. Type conversions can take advantage of certain features of type hierarchies or data representations. Two important aspects of a type conversion are whether it happens ''implicitly'' (automatically) or ''explicitly'', and whether the underlying data representation is converted from one representation into another, or a given representation is merely ''reinterpreted'' as the representation of another data type. In general, both primitive and compound data types can be converted. Each programming language has its own rules on how types can be converted. Languages with strong typing typically do little implicit conversion and discourage the reinterpretation of representations, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precision (arithmetic)
Significant figures (also known as the significant digits, ''precision'' or ''resolution'') of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expressing the result of a measurement (e.g., length, pressure, volume, or mass) has more digits than the number of digits allowed by the measurement resolution, then only as many digits as allowed by the measurement resolution are reliable, and so only these can be significant figures. For example, if a length measurement gives 114.8 mm while the smallest interval between marks on the ruler used in the measurement is 1 mm, then the first three digits (1, 1, and 4, showing 114 mm) are certain and so they are significant figures. Digits which are uncertain but ''reliable'' are also considered significant figures. In this example, the last digit (8, which adds 0.8 mm) is also considered a significant figure even though there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significand
The significand (also mantissa or coefficient, sometimes also argument, or ambiguously fraction or characteristic) is part of a number in scientific notation or in floating-point representation, consisting of its significant digits. Depending on the interpretation of the exponent, the significand may represent an integer or a fraction. Example The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10−2 power term, also called characteristics, where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic: : 123.45 = 12345 × 10−2. The same value can also be represented in normalized form with 1.2345 as the fractional coefficient, and +2 as the exponent (and 10 as the base): : 123.45 = 1.2345 × 10+2. Schmid, however, called this representation with a significand ranging between 1.0 and 10 a modified normalized form. For base 2, this 1.xxxx form is also called a normalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponent
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\ ex& = \underbrace_ \times \underbrace_ \\ ex& = b^n \times b^m \end In other words, when multiplying a base raised to one exp ... [...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, although 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. In the two's complement representation, the sign bit has the weight where is the number of bits. In the ones' complement representation, the most negative value is , but there are two representations of zero, one for each value of the sign bit. In a sign-and-magnitude representation of numbers, the value o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed-precision Arithmetic
Mixed-precision arithmetic is a form of floating-point arithmetic that uses numbers with varying widths in a single operation. Arithmetic A common usage of mixed-precision arithmetic is for operating on inaccurate numbers with a small width and expanding them to a larger, more accurate representation. For example, two half-precision or bfloat16 (16-bit) floating-point numbers may be multiplied together to result in a more accurate single-precision (32-bit) float. In this way, mixed-precision arithmetic approximates arbitrary-precision arithmetic, albeit with a low number of possible precisions. Mixed-precision arithmetic is touted in the field of machine learning, since gradient descent algorithms can use coarse and efficient half-precision floats for certain tasks, but can be more accurate if they use more precise but slower single- or double-precision floats. Some platforms, including Nvidia and AMD GPUs, provide mixed-precision arithmetic for this purpose, using coarse floats ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CUDA
CUDA (or Compute Unified Device Architecture) is a parallel computing platform and application programming interface (API) that allows software to use certain types of graphics processing units (GPUs) for general purpose processing, an approach called general-purpose computing on GPUs (GPGPU). CUDA is a software layer that gives direct access to the GPU's virtual instruction set and parallel computational elements, for the execution of compute kernels. CUDA is designed to work with programming languages such as C, C++, and Fortran. This accessibility makes it easier for specialists in parallel programming to use GPU resources, in contrast to prior APIs like Direct3D and OpenGL, which required advanced skills in graphics programming. CUDA-powered GPUs also support programming frameworks such as OpenMP, OpenACC and OpenCL; and HIP by compiling such code to CUDA. CUDA was created by Nvidia. When it was first introduced, the name was an acronym for Compute Unified Device Architectur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenCL
OpenCL (Open Computing Language) is a framework for writing programs that execute across heterogeneous platforms consisting of central processing units (CPUs), graphics processing units (GPUs), digital signal processors (DSPs), field-programmable gate arrays (FPGAs) and other processors or hardware accelerators. OpenCL specifies programming languages (based on C99, C++14 and C++17) for programming these devices and application programming interfaces (APIs) to control the platform and execute programs on the compute devices. OpenCL provides a standard interface for parallel computing using task- and data-based parallelism. OpenCL is an open standard maintained by the non-profit technology consortium Khronos Group. Conformant implementations are available from Altera, AMD, ARM, Creative, IBM, Imagination, Intel, Nvidia, Qualcomm, Samsung, Vivante, Xilinx, and ZiiLABS. Overview OpenCL views a computing system as consisting of a number of ''compute devices'', which migh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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