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.[1] It is a minor revision of the previous version, incorporating mainly clarifications, defect fixes and new recommended operations.
The IEEE Standard for Floating-Point Arithmetic (IEEE754) is a technical standard for floating-point arithmetic established in 1985 by the Institute...
such as the result of 0/0. Systematic use of NaNs was introduced by the IEEE754 floating-point standard in 1985, along with the representation of other...
condition, saves state, and switches control. Exception handling in the IEEE754 floating-point standard refers in general to exceptional conditions and...
implementations make better use of available computer hardware, such as IEEE754-1985 floating-point arithmetic, and compiler technology. The C11 version...
Motorola 68881 80-bit formats meet the requirements of the IEEE754-1985 double extended format, as does the IEEE754 128-bit binary format. The x86 extended precision...
usually encoded as +0, but can still be represented by +0, −0, or 0. The IEEE754 standard for floating-point arithmetic (presently used by most computers...
for interchange with other systems. This was subsequently addressed in IEEE754-2008, which standardized the encoding of decimal floating-point data, albeit...
of IEEE754. In casual discussions the terms subnormal and denormal are often used interchangeably, in part because there are no denormalized IEEE binary...
creating the original IEEE754 specification. Kahan continued his contributions to the IEEE754 revision that led to the current IEEE754 standard. In the...
In particular, the current IEEE754 standard does not mention it. Mantissa (logarithm) The term fraction is used in IEEE754-1985 with a different meaning:...
Electrical and Electronics Engineers Standards Association (IEEE SA) is an operating unit within IEEE that develops global standards in a broad range of industries...
power functions for the revision of the IEEE754 standard, May 2007.) "Re: A vague specification". grouper.ieee.org. Archived from the original on 2017-11-14...
was abandoned during the move to QuickBASIC 4, which used the standard IEEE754 format, introduced a few years earlier. Bill Gates and Paul Allen were...
the square root of a 32-bit floating-point number x {\displaystyle x} in IEEE754 floating-point format. The algorithm is best known for its implementation...
included on the 1981 IBM PC motherboard. Development of the 8087 led to the IEEE754-1985 standard for floating-point arithmetic. The available speed version...
demonstrate the properties and structures of floating-point arithmetic and IEEE754 numbers. Minifloats with 16 bits are half-precision numbers (opposed to...
XDR standard uses big-endian IEEE754 as its representation. It may therefore appear strange that the widespread IEEE754 floating-point standard does...
makes no distinction between integer and floating-point. JavaScript uses IEEE-754 double-precision floating-point format for all its numeric values (later...
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