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IEEE 754-1985 [1] is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. [2] During its 23 years, it was the most widely used format for floating-point computation.
An unaugmented floating-point system would contain only normalized numbers (indicated in red). Allowing denormalized numbers (blue) extends the system's range. 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.
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).
IEEE 754 specifies additional floating-point types, such as 64-bit base-2 double 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 properties of ...
OpenCL also supports half-precision floating point numbers with the half datatype on IEEE 754-2008 half-precision storage format. [21] As of 2024, Rust is currently working on adding a new f16 type for IEEE half-precision 16-bit floats. [22] Julia provides support for half-precision floating point numbers with the Float16 type. [23]
The new IEEE 754 (formally IEEE Std 754-2008, the IEEE Standard for Floating-Point Arithmetic) was published by the IEEE Computer Society on 29 August 2008, and is available from the IEEE Xplore website [4] This standard replaces IEEE 754-1985. IEEE 854, the Radix-Independent floating-point standard was withdrawn in December 2008.
underflow, set if the rounded value is tiny (as specified in IEEE 754) and inexact (or maybe limited to if it has denormalization loss, as per the 1985 version of IEEE 754), returning a subnormal value including the zeros. overflow, set if the absolute value of the rounded value is too large to be represented. An infinity or maximal finite ...
The IEEE 754 standard defines precision as the number of digits available to represent real numbers. A programming language can include single precision (32 bits), double precision (64 bits), and quadruple precision (128 bits).