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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] |
Computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, engineering, mathematical, technological and social aspects. Major computing disciplines include computer engineering, computer science, cybersecurity, data science, information systems, information technology and software engineering. The term "computing" is also synonymous with counting and calculating. In earlier times, it was used in reference to the action performed by mechanical computing machines, and before that, to human computers. History The history of computing is longer than the history of computing hardware and includes the history of methods intended for pen and paper (or for chalk and slate) with or without the aid of tables. Computing is intimately tied to the representation of numbers, though mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
−0
Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are identical. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero), regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the ''sign and magnitude'' and ''ones' complement'' signed number representations for integers, and in most floating-point number representations. The number 0 is usually encoded as +0, but can be represented by either +0 or −0. The IEEE 754 standard for floating-point arithmetic (presently used by most computers and programming languages that support floating-point numbers) requires both +0 and −0. Real arithmetic with signed zeros can be considered a variant of the extended real number line such that 1/−0 = −∞ and 1/+0 = +∞; division is only und ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer International Publishing AG
Springer Nature or the Springer Nature Group is a German-British academic publishing company created by the May 2015 merger of Springer Science+Business Media and Holtzbrinck Publishing Group's Nature Publishing Group, Palgrave Macmillan, and Macmillan Education. History The company originates from a number of journals and publishing houses, notably Springer-Verlag, which was founded in 1842 by Julius Springer in Berlin (the grandfather of Bernhard Springer who founded Springer Publishing in 1950 in New York), Nature Publishing Group Nature Portfolio (formerly known as Nature Publishing Group and Nature Research) is a division of the international scientific publishing company Springer Nature that publishes academic journals, magazines, online databases, and services in scie ... which has published ''Nature (journal) , Nature'' since 1869, and Macmillan Education, which goes back to Macmillan Publishers founded in 1843. Springer Nature was formed in 2015 by the merger of Natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Notation
Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators it is usually known as "SCI" display mode. In scientific notation, nonzero numbers are written in the form or ''m'' times ten raised to the power of ''n'', where ''n'' is an integer, and the coefficient ''m'' is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer ''n'' is called the exponent and the real number ''m'' is called the '' significand'' or ''mantissa''. The term "mantissa" can be ambiguous where logarithms are involved, because it is ... [...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 compar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arbitrary-precision Arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision. Several modern programming languages have built-in support for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required. It should not be conf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two's Complement
Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian numbers, rightmost bit in little-endian numbers) to indicate whether the binary number is positive or negative (the sign). It is used in computer science as the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. When the most significant bit is a one, the number is signed as negative. . Two's complement is executed by 1) inverting (i.e. flipping) all bits, then 2) adding a place value of 1 to the inverted number. For example, say the number −6 is of interest. +6 in binary is 0110 (the leftmost most significant bit is needed for the sign; positive 6 is not 110 because it would be interpreted as -2). Step one is to flip all bits, yielding 1001. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apple Inc
Apple Inc. is an American multinational technology company headquartered in Cupertino, California, United States. Apple is the largest technology company by revenue (totaling in 2021) and, as of June 2022, is the world's biggest company by market capitalization, the fourth-largest personal computer vendor by unit sales and second-largest mobile phone manufacturer. It is one of the Big Five American information technology companies, alongside Alphabet, Amazon, Meta, and Microsoft. Apple was founded as Apple Computer Company on April 1, 1976, by Steve Wozniak, Steve Jobs and Ronald Wayne to develop and sell Wozniak's Apple I personal computer. It was incorporated by Jobs and Wozniak as Apple Computer, Inc. in 1977 and the company's next computer, the Apple II, became a best seller and one of the first mass-produced microcomputers. Apple went public in 1980 to instant financial success. The company developed computers featuring innovative graphical user inter ... [...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 One 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 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+1, and this value rounds to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Precision
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 and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexadecimal
In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexadecimal uses 16 distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" (or alternatively "a"–"f") to represent values from 10 to 15. Software developers and system designers widely use hexadecimal numbers because they provide a human-friendly representation of binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble). For example, an 8-bit byte can have values ranging from 00000000 to 11111111 in binary form, which can be conveniently represented as 00 to FF in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value would be expressed in hexadecimal as . In programming, a number o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
