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Decimal128
In computing, decimal128 is a decimal floating-point computer numbering format that occupies 16 bytes (128 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Decimal128 supports 34 decimal digits of significand and an exponent range of −6143 to +6144, i.e. to . (Equivalently, to .) Therefore, decimal128 has the greatest range of values compared with other IEEE basic floating-point formats. Because the significand is not normalized, most values with less than 34 significant digits have multiple possible representations; , etc. Zero has possible representations ( if both signed zeros are included). Decimal128 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 decimal128 values IEEE 754 allows two alternative representation methods ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Integer Decimal
The IEEE 754-2008 standard includes decimal floating-point number formats in which the significand and the exponent (and the payloads of NaNs) can be encoded in two ways, referred to as binary encoding and ''decimal encoding''. Both formats break a number down into a sign bit ''s'', an exponent ''q'' (between ''q''min and ''q''max), and a ''p''-digit significand ''c'' (between 0 and 10''p''−1). The value encoded is (−1)''s''×10''q''×''c''. In both formats the range of possible values is identical, but they differ in how the significand ''c'' is represented. In the decimal encoding, it is encoded as a series of ''p'' decimal digits (using the densely packed decimal (DPD) encoding). This makes conversion to decimal form efficient, but requires a specialized decimal ALU to process. In the binary integer decimal (BID) encoding, it is encoded as a binary number. Format Using the fact that 210 = 1024 is only slightly more than 103 = 1000, 3''n''-digit decimal numbers ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal Floating-point
Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base-2) fractions. The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with 8 decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on. This wider range can dramatically slow the accumulation of rounding errors during successive calculations; for example, the Kahan summation alg ... [...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] |
Primitive Data Type
In computer science, primitive data types are a set of basic data types from which all other data types are constructed. Specifically it often refers to the limited set of data representations in use by a particular processor, which all compiled programs must use. Most processors support a similar set of primitive data types, although the specific representations vary. More generally, "primitive data types" may refer to the standard data types built into a programming language. Data types which are not primitive are referred to as ''derived'' or ''composite''. Primitive types are almost always value types, but composite types may also be value types. Common primitive data types The Java virtual machine's set of primitive data types is: * Integer types with a variety of ranges and precisions (byte, short, int, long, char) * Floating-point number with single or double precisions; (float, double) * Boolean, logical values true and false. (boolean) * A value referring to an execu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ISO/IEC 10967
ISO/IEC 10967, Language independent arithmetic (LIA), is a series of standards on computer arithmetic. It is compatible with ISO/IEC/IEEE 60559:2011, more known as IEEE 754-2008, and much of the specifications are for IEEE 754 special values (though such values are not required by LIA itself, unless the parameter ''iec559'' is true). It was developed by the working group ISO/IEC JTC1/SC22/WG11, which was disbanded in 2011. LIA consists of three parts: * Part 1: ''Integer and floating point arithmetic'', second edition published 2012. * Part 2: ''Elementary numerical functions'', first edition published 2001. * Part 3: ''Complex integer and floating point arithmetic and complex elementary numerical functions'', first edition published 2006. Parts Part 1 Part 1 deals with the basic integer and floating point datatypes (for multiple radices, including 2 and 10), but unlike IEEE 754-2008 not the representation of the values. Part 1 also deals with basic arithmetic, including compari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Don't Care
In digital logic, a don't-care term (abbreviated DC, historically also known as ''redundancies'', ''irrelevancies'', ''optional entries'', ''invalid combinations'', ''vacuous combinations'', ''forbidden combinations'', ''unused states'' or ''logical remainders'') for a function is an input-sequence (a series of bits) for which the function output does not matter. An input that is known never to occur is a can't-happen term. Both these types of conditions are treated the same way in logic design and may be referred to collectively as ''don't-care conditions'' for brevity. The designer of a logic circuit to implement the function need not care about such inputs, but can choose the circuit's output arbitrarily, usually such that the simplest circuit results ( minimization). Don't-care terms are important to consider in minimizing logic circuit design, including graphical methods like Karnaugh–Veitch maps and algebraic methods such as the Quine–McCluskey algorithm. In 1958, S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhäuser
Birkhäuser was a Swiss publisher founded in 1879 by Emil Birkhäuser. It was acquired by Springer Science+Business Media in 1985. Today it is an imprint used by two companies in unrelated fields: * Springer continues to publish science (particularly: history of science, geosciences, computer science) and mathematics books and journals under the Birkhäuser imprint (with a leaf logo) sometimes called Birkhäuser Science. * Birkhäuser Verlag – an architecture and design publishing company was (re)created in 2010 when Springer sold its design and architecture segment to ACTAR. The resulting Spanish-Swiss company was then called ActarBirkhäuser. After a bankruptcy, in 2012 Birkhäuser Verlag was sold again, this time to De Gruyter. Additionally, the Reinach-based printer Birkhäuser+GBC operates independently of the above, being now owned by ''Basler Zeitung''. History The original Swiss publishers program focused on regional literature. In the 1920s the sons of Emil Birkhà ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Declet (computing)
In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure information contained in messages and the entropy of random variables. The most commonly used units of data storage capacity are the bit, the capacity of a system that has only two states, and the byte (or octet), which is equivalent to eight bits. Multiples of these units can be formed from these with the SI prefixes (power-of-ten prefixes) or the newer IEC binary prefixes (power-of-two prefixes). Primary units In 1928, Ralph Hartley observed a fundamental storage principle, which was further formalized by Claude Shannon in 1945: the information that can be stored in a system is proportional to the logarithm of ''N'' possible states of that system, denoted . Changing the base of the logarithm from ''b'' to a diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal64
In computing, decimal64 is a decimal floating-point computer numbering format that occupies 8 bytes (64 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Decimal64 supports 16 decimal digits of significand and an exponent range of −383 to +384, i.e. to . (Equivalently, to .) In contrast, the corresponding binary format, which is the most commonly used type, has an approximate range of to . Because the significand is not normalized, most values with less than 16 significant digits have multiple possible representations; , etc. Zero has 768 possible representations (1536 if both signed zeros are included). Decimal64 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 decimal64 values IEEE 754 allows two alternative representation methods ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal32
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 dec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subnormal Numbers
In computer science, subnormal numbers are the subset of denormalized numbers (sometimes called denormals) that fill the underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than the smallest normal number is ''subnormal''. :: ''Usage note: in some older documents (especially standards documents such as the initial releases of IEEE 754 and 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.'' In a normal floating-point value, there are no leading zeros in the significand ( mantissa); rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as ). Conversely, a denormalized floating point value has a significand with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was 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 l'Hôpital and 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 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 infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
