IEEE Floating Point Standard - определение. Что такое IEEE Floating Point Standard
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Что (кто) такое IEEE Floating Point Standard - определение

IEEE STANDARD FOR FLOATING-POINT ARITHMETIC
IEEE Floating Point Standard; Ieee float; IEEE floating-point arithmetic; IEEE floating-point; IEC 60559; IEC 559; IEEE floating point number; IEEE floating-point number; IEEE-754; IEEE floating point standard; IEEE754; IEEE floating-point standard; Ieee floating point; IEEE float; IEEE floats; IEEE floating points; ISO/IEC/IEEE 60559:2011; IEEE arithmetic; Octuple-precision floating-point; ISO/IEC/IEEE 60559:2011-06; ISO/IEC/IEEE 60559; IEEE 754 format; IEEE floating point; IEEE 754-2019; IEEE 754-2019 revision; IEEE augmented arithmetic operation; IEEE 754 augmented arithmetic operation; IEEE 754 recommended operations; IEEE 754 recommended operation; ISO/IEC 60559; IEEE 754 standard
  • none
  • Precision of binary32 and binary64 in the range 10<sup>−12</sup> to 10<sup>12</sup>
  • [[William Kahan]]. A primary architect of the Intel [[80x87]] floating-point coprocessor and IEEE 754 floating-point standard.
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IEEE Floating Point Standard         
<standard, mathematics> (IEEE 754) "IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985)" or IEC 559: "Binary floating-point arithmetic for microprocessor systems". A standard, used by many CPUs and FPUs, which defines formats for representing floating-point numbers; representations of special values (e.g. infinity, very small values, NaN); five exceptions, when they occur, and what happens when they do occur; four rounding modes; and a set of floating-point operations that will work identically on any conforming system. IEEE 754 specifies formats for representing floating-point values: single-precision (32-bit) is required, double-precision (64-bit) is optional. The standard also mentions that some implementations may include single-extended precision (80-bit) and double-extended precision (128-bit) formats. [On-line document?] (2003-06-17)
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.
IEC 559         
IEEE 754         
floating-point         
COMPUTER FORMAT FOR REPRESENTING RATIONAL NUMBERS
Floating-point; Floating-point number; Floating point number; Hidden bit; Floating point type; Floating point numbers; Floating point arithmetic; Floating-point error; Floating point value; Numeric (data type); Floating point error; Floating-point math; Float (computing); Floating point exception; Floating-Point; Finite precision arithmetics; Floating-point numbers; Floating decimal point; Floating point format; Floating-point format; Floating point representation; Floating-point representation; Floating-point arithmetics; Floating point arithmetics; Floating point; Binary floating point; Assumed bit; Implicit bit; Assumed bit (floating point); Hidden bit (floating point); Implicit bit (floating point); Leading bit (floating point); Implicit leading bit (floating point); Implicit leading bit; Implicit leading bit convention; Assumed bit convention; Leading bit convention; Implicit bit convention; Hidden bit convention; Hidden bit rule; Implicit bit rule; Implicit leading bit rule; Assumed bit rule; Leading bit rule; Binary floating-point; Octal floating point; Octal floating-point; Binary floating-point arithmetic; Binary floating-point number; Octal floating-point number; Octal floating-point arithmetic; Base 2 floating point; Base-2 floating point; Radix-2 floating point; Radix 2 floating point; Base 8 floating point; Base-8 floating point; Radix-8 floating point; Radix 8 floating point; Binary512; Radix 65536 floating point; Radix-65536 floating point; Base 65536 floating point; Base-65536 floating point; Base-256 floating point; Quaternary floating point; Base 256 floating point; Radix 256 floating point; Radix-256 floating point; Base 4 floating point; Base-4 floating point; Radix 4 floating point; Radix-4 floating point; Binary floating point number; Representable floating-point number; Fast math; Floating point math; Binary floating-point number system; Binary floating point number system; Binary floating point numbering system; Binary floating-point numbering system
<programming, mathematics> A number representation consisting of a mantissa, M, an exponent, E, and a radix (or "base"). The number represented is M*R^E where R is the radix. In science and engineering, exponential notation or scientific notation uses a radix of ten so, for example, the number 93,000,000 might be written 9.3 x 10^7 (where ^7 is superscript 7). In computer hardware, floating point numbers are usually represented with a radix of two since the mantissa and exponent are stored in binary, though many different representations could be used. The IEEE specify a standard representation which is used by many hardware floating-point systems. Non-zero numbers are normalised so that the binary point is immediately before the most significant bit of the mantissa. Since the number is non-zero, this bit must be a one so it need not be stored. A fixed "bias" is added to the exponent so that positive and negative exponents can be represented without a sign bit. Finally, extreme values of exponent (all zeros and all ones) are used to represent special numbers like zero and positive and negative infinity. In programming languages with explicit typing, floating-point types are introduced with the keyword "float" or sometimes "double" for a higher precision type. See also floating-point accelerator, floating-point unit. Opposite: fixed-point. (2008-06-13)
floating-point         
COMPUTER FORMAT FOR REPRESENTING RATIONAL NUMBERS
Floating-point; Floating-point number; Floating point number; Hidden bit; Floating point type; Floating point numbers; Floating point arithmetic; Floating-point error; Floating point value; Numeric (data type); Floating point error; Floating-point math; Float (computing); Floating point exception; Floating-Point; Finite precision arithmetics; Floating-point numbers; Floating decimal point; Floating point format; Floating-point format; Floating point representation; Floating-point representation; Floating-point arithmetics; Floating point arithmetics; Floating point; Binary floating point; Assumed bit; Implicit bit; Assumed bit (floating point); Hidden bit (floating point); Implicit bit (floating point); Leading bit (floating point); Implicit leading bit (floating point); Implicit leading bit; Implicit leading bit convention; Assumed bit convention; Leading bit convention; Implicit bit convention; Hidden bit convention; Hidden bit rule; Implicit bit rule; Implicit leading bit rule; Assumed bit rule; Leading bit rule; Binary floating-point; Octal floating point; Octal floating-point; Binary floating-point arithmetic; Binary floating-point number; Octal floating-point number; Octal floating-point arithmetic; Base 2 floating point; Base-2 floating point; Radix-2 floating point; Radix 2 floating point; Base 8 floating point; Base-8 floating point; Radix-8 floating point; Radix 8 floating point; Binary512; Radix 65536 floating point; Radix-65536 floating point; Base 65536 floating point; Base-65536 floating point; Base-256 floating point; Quaternary floating point; Base 256 floating point; Radix 256 floating point; Radix-256 floating point; Base 4 floating point; Base-4 floating point; Radix 4 floating point; Radix-4 floating point; Binary floating point number; Representable floating-point number; Fast math; Floating point math; Binary floating-point number system; Binary floating point number system; Binary floating point numbering system; Binary floating-point numbering system
¦ noun [as modifier] Computing denoting a mode of representing numbers as two sequences of bits, one representing the digits in the number and the other an exponent which determines the position of the radix point.
Floating-point arithmetic         
COMPUTER FORMAT FOR REPRESENTING RATIONAL NUMBERS
Floating-point; Floating-point number; Floating point number; Hidden bit; Floating point type; Floating point numbers; Floating point arithmetic; Floating-point error; Floating point value; Numeric (data type); Floating point error; Floating-point math; Float (computing); Floating point exception; Floating-Point; Finite precision arithmetics; Floating-point numbers; Floating decimal point; Floating point format; Floating-point format; Floating point representation; Floating-point representation; Floating-point arithmetics; Floating point arithmetics; Floating point; Binary floating point; Assumed bit; Implicit bit; Assumed bit (floating point); Hidden bit (floating point); Implicit bit (floating point); Leading bit (floating point); Implicit leading bit (floating point); Implicit leading bit; Implicit leading bit convention; Assumed bit convention; Leading bit convention; Implicit bit convention; Hidden bit convention; Hidden bit rule; Implicit bit rule; Implicit leading bit rule; Assumed bit rule; Leading bit rule; Binary floating-point; Octal floating point; Octal floating-point; Binary floating-point arithmetic; Binary floating-point number; Octal floating-point number; Octal floating-point arithmetic; Base 2 floating point; Base-2 floating point; Radix-2 floating point; Radix 2 floating point; Base 8 floating point; Base-8 floating point; Radix-8 floating point; Radix 8 floating point; Binary512; Radix 65536 floating point; Radix-65536 floating point; Base 65536 floating point; Base-65536 floating point; Base-256 floating point; Quaternary floating point; Base 256 floating point; Radix 256 floating point; Radix-256 floating point; Base 4 floating point; Base-4 floating point; Radix 4 floating point; Radix-4 floating point; Binary floating point number; Representable floating-point number; Fast math; Floating point math; Binary floating-point number system; Binary floating point number system; Binary floating point numbering system; Binary floating-point numbering system
In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. For this reason, floating-point computation is often used in systems with very small and very large real numbers that require fast processing times.
Floating-point unit         
COPROCESSOR FOR FLOATING POINT ARITHMETIC
Floating Point Unit; Floating-Point Processor; Math coprocessor; Floating point processor; Floating-Point Unit; Floating point unit; Floating-point emulation; Floating point emulation; FP emulation; FP emulator; FPU emulation; FPU emulator; Floating-point emulator; Floating point emulator; Floating-point unit emulator; Floating point unit emulator; Floating-point unit emulation; Floating point unit emulation; Floating point software emulation; Floating-point software emulation; Floating point software emulator; Floating-point software emulator; FP software emulation; FP software emulator; Floating-point emulation software; Floating point emulation software; FP emulation software; Floating-point emulation software routine; Floating point emulation software routine; FP emulation software routine
A floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating-point numbers. Typical operations are addition, subtraction, multiplication, division, and square root.
Floating-Point Unit         
COPROCESSOR FOR FLOATING POINT ARITHMETIC
Floating Point Unit; Floating-Point Processor; Math coprocessor; Floating point processor; Floating-Point Unit; Floating point unit; Floating-point emulation; Floating point emulation; FP emulation; FP emulator; FPU emulation; FPU emulator; Floating-point emulator; Floating point emulator; Floating-point unit emulator; Floating point unit emulator; Floating-point unit emulation; Floating point unit emulation; Floating point software emulation; Floating-point software emulation; Floating point software emulator; Floating-point software emulator; FP software emulation; FP software emulator; Floating-point emulation software; Floating point emulation software; FP emulation software; Floating-point emulation software routine; Floating point emulation software routine; FP emulation software routine
<hardware> (FPU) A floating-point accelerator, usually in a single integrated circuit, possible on the same IC as the central processing unit. (1994-10-27)
802.3         
COLLECTION OF STANDARDS FOR WIRED ETHERNET
802.3; IEE 802.3; IEEE 802.3-2002; IEEE 802.3-2005; IEEE 802.3-2008; IEEE 802.3 standard; IEEE 802·3; Ieee802.3; IEEE 802.3-1998; IEEE 802.3-2012; IEEE 802.3-2015; IEEE 802.3-1983; 802.3c; IEEE 802.3c; 802.3q; IEEE 802.3q

Википедия

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
  • exception handling: indications of exceptional conditions (such as division by zero, overflow, etc.)

IEEE 754-2008, published in August 2008, includes nearly all of the original IEEE 754-1985 standard, plus the IEEE 854-1987 Standard for Radix-Independent Floating-Point Arithmetic. The current version, IEEE 754-2019, was published in July 2019. It is a minor revision of the previous version, incorporating mainly clarifications, defect fixes and new recommended operations.